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Average price 2017-09-15
From Annette:
If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price
Answered by Penny Nom.
Differentiate y = x^x^x 2017-03-19
From Nafis:
differentiate y = x^x^x
Answered by Penny Nom.
The derivative of the inverse of a function 2016-10-28
From Kate:
Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^-1(4) if f(3)=4 and f'(3)=1/7

Answered by Penny Nom.
Subtraction of two numbers in different bases 2016-10-07
From Wica:

So happy I found this site. I am having problems with bases. My question is :
Please perform the subtraction between two number over different bases :
A. (5874)base 12 - (216)base 9
B. (216)base 9 - (5874)base 12

Answered by Penny Nom.
Implicit differentiation 2016-06-06
From Pranay:
Is a circle x^2+y^2=2 a function? If it is not a function, why is it possible to do implicit differentiation on it?

Answered by Penny Nom.
A tangent line to a parabola 2015-12-02
From pei:
Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M.
Answered by Penny Nom.
The derivative of x^1/3 2015-11-08
From omar:
hi can help me
am teacher ask me about x^1/3 Derivation definition .

Answered by Penny Nom.
Two cars approaching an intersection 2015-04-16
From Engabu:
Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection?
Answered by Penny Nom.
Integers in different bases 2015-03-05
From Michael:
Let k be a positive integer so that 28 (subscript)k = 132 (subscript)5
Answered by Penny Nom.
f(x)=(x^2-1)/(x-1) 2015-02-21
From Ahmed:
Is f(x)=[(x^2-1)/(x-1) and x=2 at x=1] differentiable at x=1 ? Why ?
Answered by Penny Nom.
Differentiate ln[x(2x-4)^1/2] 2014-06-28
From Igwe:
If y=In[x(2x-4)^1/2],find dy/dx at x=3
Answered by Penny Nom.
A tangent of the curve (x/a)^n+(y/b)^n =2 2014-04-15
From sudhir:
the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is
Answered by Penny Nom.
A number with all the digits different 2014-02-07
From Jon:
I'm not a mathematician but just curious. Is there a name for a number of up to ten digits where each digit is different, i.e the equivalent of an isogram in linguistics? My online banking gives me a random 8-digit number each time I log on and it is rare to get one of the type I refer to. There must be calculable odds, but I'm only allowed one question!
Thanks in advance

Answered by Harley Weston.
Differentiate x^x - 2^sinx 2013-08-09
From tarun:
derivative of x^x - 2^sinx
Answered by Penny Nom.
f(x) + f ''''(x)=0 2013-03-05
From Andreea:
Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something.
Answered by Brennan Yaremko.
The multiplication table for the different bases 2013-02-01
From sylvia:
I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers.
Answered by Penny Nom.
The derivative of y = sin (30º + x) 2012-11-07
From Saskia:
derivative of y = sin (30º + x)
Answered by Harley Weston.
An implicit differentiation problem 2012-10-26
From Katie:
find y' of x^2y-2y^3=3x+2y
Answered by Harley Weston.
Differentiation rules 2012-10-23
From Morgan:
Use the derivative rules to differentiate each of the following:
1. f(x)=1/x-1
2. f(x)= sqrt(x)

Answered by Penny Nom.
The derivative of 2sin cubed x - 3 sin x 2012-03-25
From holly:
suppose f(x) = 2sin cubed x - 3 sin x

show that f 1(x) = -3 cos x cos 2x

Answered by Harley Weston.
Integral 1/(25-x^2)^3/2 2012-02-22
From John:
Integral 1/(25-x^2)^3/2
Answered by Harley Weston.
Dt[sin t tan (t^2+1)] 2012-02-21
From Ayu:
Dt[sin t tan (t^2+1)]

Answered by Harley Weston.
Notation for the second derivative 2012-02-06
From Shafira:
In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2?
Answered by Robert Dawson.
The derivative of x^-(1/2) 2012-01-14
From Eric:
I have an problem figuring out the derivative of the negative square root of x i.e. x^-(1/2) using the first principle.
Could someone please show me?
Thanks in advance!

Answered by Harley Weston.
The number of digits in a number base m 2011-12-22
From Jash:
Assume there is a number system of base m.

The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b).

In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant.

Find m.

Answered by Robert Dawson.
Implicit differentiation 2011-10-20
From Monica:
Find dy/dx in terms of x and y, if sin(xy)=(x^2)-y.
Answered by Penny Nom.
The derivative of f(x) = (x+1)^1/2 2011-09-05
From Carla:
Find the derivative using the limit process of
f(x) = (x+1)^1/2

Answered by Harley Weston.
Differentiable on an interval 2010-08-12
From Dave:
Hi I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help.
Answered by Robert Dawson.
The rate of change of y with respect to x 2010-04-29
From Tom:
I just had a quick calc question about wording that wasn't ever addressed in class. When the book says "the rate of change of y with respect to x", should it be considered how fast y is changing in comparison to x?

I ask because the textbook says that "y is changing 3 times faster than x, so the rate of change of y with respect to x is 3." I'm use to rate being like velocity, as in units of distance per units of time. All we're told in class is that it's the slope of the tangent line, I was hoping you could clarify for me what exactly is meant by the wording of a "rate of change of something with respect to something else". More specifically, what "rate" and "with respect to" mean within this context?

Thanks for your time

Answered by Harley Weston.
The derivative of cos^3x 2010-04-06
From Erson:
Find y' of the given function: y = cos^3x.
Answered by Harley Weston.
The nth derivative of x^(n-1) log x 2010-03-10
From shambodeb:
This is a successive differentiation problem by Leibnitz theorem

If y = xn-1 log x ; Proof nth derivative y(n) = (n-1)!/x

Answered by Harley Weston.
Painting a dome 2009-10-30
From Jessica:
A hemispherical dome with a radius of 50 ft will be given a coat of paint .01 inch thick. The Contractor for the job wants to estimate the number of gallons of paint needed. Use a differential to obtain an estimate (231 cubic inches/gallon) HINT: Approximate the change in volume of hemisphere corresponding to increase of .01 inch in the radius.
Answered by Robert Dawson.
Differentiating y= square root(x-1) 2009-09-29
From edith:
describe the x-values at which f is differentiable.
y= square root(x-1)

Answered by Penny Nom.
Maximum Volume of a Cylinder Inscribed in a Sphere 2009-06-18
From Jim:
Hello I have a hard time finishing this question: A right circular cylinder has to be designed to sit inside a sphere of radius 6 meters so that each top and bottom of the cylinder touches the sphere along its complete circular edge. What are the dimensions of the cylinder of max volume and what is the volume?
Answered by Janice Cotcher.
differentiate y sin[x^2]=x sin[y^2] 2009-05-11
From mamiriri:
derivate y sin[x^2]=x sin[y^2]
Answered by Harley Weston.
Implicit differentiation 2009-03-01
From Emily:
determine the derivative y' at the point (1,0)
y= ln(x^2+y^2)

y'(1)= ??

Answered by Stephen La Rocque.
Multiplying in different bases 2009-02-25
From Susan:
11 base 2 X 22 base 3 + 33 base 4 = _________ base 5
Answered by Robert Dawson.
Implicit differentiation 2009-02-18
From Sunny:
Find slope of the tangent line to the curve 2(x^2+y^2)2=25(x^2–y^2) at (3,-1)
Answered by Robert Dawson and Harley Weston.
In what base is 3x3= 10? 2009-02-14
From David:
In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one?
Answered by Penny Nom.
What's the derivative of y = e^2x-e^-2x / e^2x+e^-2x? 2009-02-02
From Heather:
What's the derivative of y = e^2x-e^-2x / e^2x+e^-2x ?
Answered by Harley Weston.
Determine y'' by implicitly differentiating twice 2009-01-04
From Walter:
Given x^3 - 3xy + y^3 = 1 , determine y'' by implicitly differentiating twice. I cannot solve this. Would you be kind enough to perform the mathematics and show the steps involved in obtaining the solution?
Answered by Harley Weston.
Division in different bases 2008-12-02
DIVIDE 538 BY 14 IN BASE 2, 3, 4 & 5
Answered by Penny.
Separating variables 2008-11-04
From Terry:
by separating variables solve the initial value problem

(x+1)y' + y = 0 y(0) = 1

Answered by Harley Weston.
Antiderivative of 1/(x(1 - x)) 2008-10-22
From Matt:
derivative of dx/(x(1-x))

From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions.

If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative.

Answered by Harley Weston.
Concavity and the second derivative 2008-10-15
From Christina:
I'm having trouble solving for a second derivative for the following graphing question.

f(x) = (X^2+2x+4)/2x

using the quotient rule, I found:
f'(x) = (x^2-4)/(2x^2)

however, using the quotient rule again I can't seem to solve it (concavity):
f''(x)=[(4x^3-(4x^3 -16x)]/4x^4

and making the equation equal to zero result in 0=4 which doesn't seem to make sense...

Answered by Penny Nom.
A different approach to a word problem 2008-10-03
From Kenneth:
Sarah's age is 2/3 of Mary's age and 3/4 of Ruth's age. The sum of their ages is 46 years. How old is each?
Answered by Penny Nom.
What is the derivative of (2^sinx)/(logbase4(2x+1))? 2008-09-16
From Jesse:
What is the derivative of (2^sinx)/(logbase4(2x+1))
Answered by Harley Weston.
Trough Filling with Water 2008-08-21
From lanny:
a triangular trough is 10 feet long, 6 feet across the top, and 3 feet deep. if water flows at the rate of 12 cubic inches per minute, find how fast the surface is rising when the water is 6 inches deep.
Answered by Janice Cotcher.
A series solution of y' = xy 2008-07-03
From sasha:
I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks

Answered by Harley Weston.
Differentiate y= (x^x^x)^x 2008-06-27
From emril:
Differentiate y= (x^x^x)^x
Answered by Harley Weston.
f(x)=sin^3(3x^2) find f ' (x) 2008-04-21
From Michael:
f(x)=sin^3(3x^2) find f ' (x)
Answered by Harley Weston.
The chain rule 2008-04-10
From joey:
pls help me to Differentiate

Answered by Harley Weston.
Differentiate 2007-12-28
From taiwo:
i am finding it difficult to use first principle to differentiate this question: y=xcos2x. can u help me.
Answered by Penny Nom.
The tangent to a curve 2007-12-10
From Christy:
I know this question is simple but I can't figure out what I'm doing wrong.
Find the equation of the tangent line to the curve 2x^2 - y^4= 1 at the point (1,1).

Answered by Penny Nom.
The derivative 2007-11-19
From ralf:
Find the derivative of the function
1-. y=1+2x8
2-. y=(1+2x )8

Answered by Harley Weston.
f(x+y) = f(x) + f(y) + 2xy 2007-11-01
From Marcia:
For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h -> 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x).
Answered by Penny Nom.
The rate of change of the concentration of a solution 2007-10-30
From Nicholas:
A barrel initially has two kg of salt dissolved in twenty liters of water. If water flows in the rate of 0.4 liters per minute and the well-mixed salt water solution flow out at the same rate, how much salt is present after 8 minutes? I tried working backwards given the answer but I can't seen to get their answer of ~1.7kg. Any help would be great! Thanks
Answered by Harley Weston.
The derivative of f(x)=1/(x-1) 2007-09-21
From Michelle:
im having trouble finding the derivative of f(x)=1/(x-1) using the f(x+h)-f(x)/h method.
Answered by Stephen La Rocque.
Differentiate x^(1/3) using first principles 2007-09-14
From Sheila:
our teacher gave us this question as a challenge and even he couldnt figure it out: Differentiate x^(1/3) [aka the cube root of x] using first principles. i know the answer is 1/(3.x^2/3), but how is it possible using first principles?
Answered by Harley Weston.
Solve y'' + y = 0 2007-07-28
From Shih-ya:
How do you solve y’’ + y = 0
Answered by Stephen La Rocque and Harley Weston.
Implicit Derivatives 2007-07-13
From Charles:
I need help computing y' by implicit differentiation the question is: y^2 + x/y + 4x^2 - 3
Answered by Stephen La Rocque.
sin|x| and cos|x| 2007-06-25
From Mac:
Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ? As far as i know, cos(x) and sin(x) is differentiable at all x.
Answered by Penny Nom and Stephen La Rocque.
The second derivative 2007-04-14
From Gerry:
In mathematical context,what do you understand by the term "Second Derivative"
Answered by Penny Nom.
What is the intensity 5m below the surface? 2007-03-31
From david:
I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help.
Answered by Penny Nom.
The period of a simple pendulum 2007-03-10
From Melissa:
The period of a simple pendulum of length L feet is given by: T=2pi(sqrt(L/g))seconds. It is assumed that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.) Answer is in seconds. Melissa
Answered by Penny Nom.
Derivatives 2007-02-01
From Jacob:
Find the derivative of: y= pi^2+x^2+3xy+sin(y^2)
Answered by Penny Nom.
Water is being pumped into the pool 2006-10-24
From Jon:
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end.

a) what percent of the pool is filled?

b) at what rate is the water level rising?

Answered by Stephen La Rocque.
Differentiate Y= sin3x + cos7x 2006-08-22
From james:
Differentiate the function of x using the basic rules.

Y= sin3x + cos7x

Answered by Stephen La Rocque.
differentiate the volume of a cylinder with V respect to h 2006-05-24
From A student:
differentiate the volume of a cylinder with V respect to h
Answered by Stephen La Rocque.
Rate of ladder falling 2006-04-30
From Harsh:
A ladder 4 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 30 cm/s, how quickly is the top of the ladder sliding down the wall when the bottom of the ladder is 2 m from the wall?
Answered by Stephen La Rocque.
Differentiation, powers and logs 2006-01-06
From Claudia:

Question: how do I find the derivative of

x* ln(x+(e^2))^2



Answered by Penny Nom.
Notation for the second derivative 2005-11-08
From Mussawar:
my question is d/dx( dy/dx) = d2y/dx2. why it is not equal to d2y/d2x.
Answered by Penny Nom.
Velocity and acceleration 2005-10-27
From Candace:
When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared- where do the units go when you make it an equation? How can a function be an area?
Answered by Harley Weston.
Can we take the derivative of independent variable 2005-10-18
From Mussawar:
why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why.
Answered by Walter Whiteley.
U'(X) - U(X) = 0; U(0) = 2 2005-09-23
From David:
Out of interest could you please answer the following questions?

U'(X) - U(X) = 0; U(0) = 2


U''(X) - U'(X) = 0; U'(0) = U(0) = 2

Answered by Harley Weston.
How do you differentiate y=(x)^(x^x)? 2005-09-14
From Calebius:
How do you differentiate y=(x)(xx)?
Answered by Penny Nom.
Logarithmic differentiation 2005-05-23
From Richard:
I need to convince myself that I understand the process of differentiating y=xx.
The specific question is that if I have to take the logarithm of both sides of the equation how can differentiate the following?
y= {(x+2)(x+2)}/{(x+1)(x+1)} - {(x+1)(x+1)}/(xx),
I have an idea that the differential of this fairly complex function is itself ... am I right or wrong.

Answered by Penny Nom.
Differentiating F(x,y) = 0 2005-01-23
From Jacob:
In calculus, we often mention to the students that if F(x,y) = 0, then we can differentiate both sides and still get an equality. The problem is that we can't perform the same operation on F(x) = 0, say x = 0, otherwise 1 = 0, which is absurd. What is the reason?
Answered by Walyer Whileley and Harley Weston.
ln(x)/x 2004-12-11
From Tina:
What is the derivative of (ln x)/x? The double derivative?
Answered by Penny Nom.
An ODE 2004-11-10
From David:
I have a question that i really cant do, it is as follows:

The ODE dy/dx + 0.5y = 0.5e^(-1.5x) ; y(5) = 2

Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6

Answered by Harley Weston.
Implicit differentiation 2004-10-24
From Emily:
If x^3+3xy+2y^3=17, then in terms of x and y, dy/dx =
Answered by Penny Nom.
differentiate Y=X^X^X 2004-09-13
From Kunle:
differentiate Y=X^X^X
Answered by Penny Nom.
The integrating factor method 2004-08-05
From A student:
Whilst using the integrating factor method, I am required to integrate a function multipled by another function.

say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.

Integral f(t)*g(t) dt or Integral exp(kt)*g(t) dt

What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k? More specifically, the problem and my attempted answer is in PDF format:

In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function.

Answered by Harley Weston.
Differentiation 2004-08-04
From A parent:
I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus:

a) f(x)=e^2^xIn(cos(8x))

b) f(x)=secx/SQRTx^4+1

Answered by Penny Nom.
Some calculus problems 2004-04-01
From Weisu:

I have questions about three word problems and one
regular problem, all dealing with derivatives.

  1. Find all points on xy=exy where the tangent line
    is horizontal.
  2. The width x of a rectangle is decreasing at 3 cm/s,
    and its length y is increasing at 5 cm/s. At what rate
    is its area A changing when x=10 and y=15?
  3. A car and a truck leave the same intersection, the
    truck heading north at 60 mph and the car heading west
    at 55 mph. At what rate is the distance between the
    car and the truck changing when the car and the truck
    are 30 miles and 40 miles from the intersection,
  4. The production P of a company satisfies the
    equation P=x2 + 0.1xy + y2, where x and y are
    the inputs. At a certain period x=10 units and y=8
    units. Estimate the change in y that should be made to
    set up a decrease of 0.5 in the input x so that the
    production remains the same.

If you could just give me some hints on these
questions, I'd really appreciate it. Thanks!

Answered by Penny Nom.
A derivative 2004-03-31
From A student:
What is the nth derivative of f(x) =(2x)/(1-(x2))?
Answered by Harley Weston.
A partial derivative 2004-03-19
From Penny Nom:
Is it possible to differentiate the following equation, if so could you please explain.


I would like the derivative of S with respect to X.

Answered by Harley Weston.
The derivative of x to the x 2004-02-14
From Cher:
what about the derivative of x to the power x?
Answered by Penny Nom.
The slope of a tangent 2003-10-01
From A student:

find the slope of the tangent to each curve at the given point

f(x)=square root 16-x, where y=5

Answered by Penny Nom.
Differentiating inverses 2002-11-20
From Amy:
f(x)= x3+x+1, a=1 find g'(a) (g = f -1). I am having trouble finding g(a).
Answered by Penny Nom.
Undetermined coefficients 2001-11-22
From Hoda:
The equation is:

y" - 2y' + y = t et + 4

We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions?

Answered by Harley Weston.
A tangent line 2001-11-21
From A student:
write an equation of the line tangent to the graph of

ey + ln(xy) = 1 + e at (e,1)

Answered by Harley Weston.
4 sinx cosy = 1 2001-10-10
From A student:
How would i differentiate the following example in terms of t (x and y are functions of t)

4 sinx cosy = 1

Answered by Claude Tardif.
(x^2-5x-6)/(x-6) 2001-10-02
From Bill:
given f(x) = (x2-5x-6)/(x-6) find f'(6).
Answered by Harley Weston.
National consumption function 2001-05-09
From Brian:
If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function.
Answered by Harley Weston.
Differentiation 2001-04-17
From Esther:
Could you please tell me what the first derivative is of the following:

y = 2/(2x+e2x)

Is it (1+xe2x)/(2x+e2x)2 or perhaps -4(1+e2x)/(2x+e2x)2 ? I am a little confused between the two!

Answered by Harley Weston.
Airflow in windpipes 2001-03-25
From Ena:
The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that:
0 < 0.5*Ro < R < Ro,
find the factor by which the radius of the windpipe contracts to give maximum flow?

Answered by Harley Weston.
A jogger 2001-03-12
From Bill:
At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes.

a) write an expression for the velocity of the jogger at time t.

b) what is the total distance traveled by the jogger in that 10-minute interval.

Answered by Harley Weston.
The domain of the derivative 2001-02-22
From Wayne:
I know that the domain of f'(x) is a subset of the domain of f(x). Is it necessarily true that the subset will have at most one less element than the domain of the original function?
Answered by Harley Wesston.
Differentiation of y = x n 2001-02-17
From Jashan:
i am studying differentation at the moment i have drawn some graphs such as y=x 2. i have found the formula for the gradient of this curve, this being 2x obtained by using differentation, but i need to know the general case for the formula where y=xn in order for me to understand this topic more throughly, i would also like to know how u derived this general formula
Answered by Harley Weston.
Find an exprression for f(x) 2001-02-07
From A 12th grade AP Calc student:
Let f be the function defined for all x > -5 and having the following properties. Find an expression for f(x).

i) f ''(x) = 1/ (x+5)1/3 for all x in the domain of f

ii) the line tangent to the graph of f at (4,2) has an angle of inclination of 45 degress.

Answered by Harley Weston.
How do you integrate secant(theta)? 2000-12-22
From Robert Williamson:
How do you integrate secant(theta)?

I know the answer is ln [sec(theta) + tan(theta)] but how do you get there?

Answered by Claude tardif.
Derivatives, there must be an easier way 2000-09-06
From Brad Goorman:
The direction read: Take the derivative of each expression.

y = {1+[x+(x2 +x3)4]5}6

Answered by Harley Weston.
A derivative problem 2000-06-04
From Jeff Ellis:
If F(x)=(4+x)(3+2x2)2(2+3x3)3, find F'(0)
Answered by Harley Weston.
Thearcius Functionius 2000-05-03
From Kevin Palmer:
With the Olympics fast approaching the networks are focusing in ona new and exciting runner from Greece. Thearcius Functionius has astounded the world with his speed. He has already established new world records in the 100 meter dash and looks to improve on those times at the 2000 Summer Olympics.

Thearcius Functionius stands a full 2 meters tall and the networks plan on placing a camera on the ground at some location after the finish line(in his lane) to film the history making run. The camera is set to film him from his knees(0.5 meters up from the ground) to 0.5 meters above his head at the instant he finishes the race. This is a total distance of two meters(the distance shown by the camera's lens).
Answered by Harley Weston.

An indefinite integral 2000-05-03
From Bonnie Null:
I am to find the indefinite integral of: (ex - e-x)2 dx
Answered by Claude Tardif.
y = x^x^x^x... 2000-04-05
From Michael Hackman:
Find the derivative of: y = x^x^x^x... on to infinity.
Answered by Claude Tardif.
A mixture problem 2000-03-06
From Rebecca Edwards:
A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t.
Answered by Harley Weston.
A calculus problem 1999-12-08
From JT Wilkins:
These are the questions:

  1. Show that there exists a unique function that meets the following requirements:

    a) f is differentiable everywhere
    b) f(0)= f'(0)= 0
    c) f(x+y)= f(x)+ f(y), for all real values of x,y

  2. Consider the function F: R-->R (All Reals)

    F(x) = 0, for x irrational & 1/q, x=p/q gcd(p,q)=1 q > 0

    a)determine the values x where f is continuous, respectively discontinuous.
    b)determine the values x when f is differentiable and for each of these values compute f'(x).

Answered by Penny Nom.
The chain rule 1999-12-03
From Jennifer Stanley:
This problem is making me dizzy. I would greatly appreciate a little help!

Express the derivative dy/dx in terms of x.

y=u^2(u-u^4)^3 and u=1/x^2
Answered by Harley Weston.

Two calculus problems 1999-12-01
From O'Sullivan:
Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help.

I've set up a ratio and tried to find the constant but am stuck.

Question #2 The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (-5,0) is on the edge of the shadow, how far above the x axis is the lamp located?

The picture shows an x and y axis with only the points -5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5.

Answered by Harley Weston.
Two derivatives 1999-11-16
From Gina Renicker:
The derivative of:

y=e(xlnx) and y=x2arctan(x1/2)
Answered by Harley Weston.

Clockwise or Counterclockwise? 1999-10-27
From Tim:
A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y
  1. Find dy/dt

  2. Does the particle travel clockwise or counterclockwise around the circle? Why?

Answered by Harley Weston.
Derivatives with logs 1999-10-26
From Kate:
What is the derivative of 5 to the 5x-2 at x equals 0.8?
Answered by Harley Weston.
Parametric Equations 1999-08-06
From Nicholas Lawton:
Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is :

Answered by Harley Weston.

A calculus problem 1999-07-22
From Nicholas Lawton:
The curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the x-axis. the point (0,9) is on the curve. Find the values of p,q and r.
Answered by Harley Weston.
Related rates 1999-05-13
From Tammy:
The sides of a rectangle increase in such a way that dz/dt=1 and dx/dt=3*dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt? (there is a picture of a rectangle with sides x and y, and they are connected by z, which cuts the rectangle in half)
Answered by Harley Weston.
Graphing the Derivative 1999-01-18
From Milena Ghebre:
This question has been nagging me for sometime now.

Is there a way of finding out the derivative of a function, just by looking at the graph of it?
Answered by Walter Whiteley.

Calculus 1999-01-16
From Kaylea Rankin:
Differentiate the following.

y = 1 /(2+3/x)
Answered by Jack LeSage and Penny Nom.

The area and the circumference of a circle. 1998-08-27
From Jason Wright:
I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me!
Answered by Walter Whiteley.
A Tightrope Walker. 1998-02-19
From Amy Zitron:
A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A....
Answered by Harley Weston.
Mathematical Induction and the Derivative 1997-03-18
From Shuling Chong:
"Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n."

Any educated tries are appreciated.
Answered by Penny Nom.

Une autre bille de rayon différent 2002-02-27
From Sarah:
une bille de 6 cm repose au fond d'1 cylindre droit dont la base est un disque de rayon 10 cm. On verse de l'eau dans le cylindre de façon à recouvrir exactement la bille. Démontrez que l'on peut remplacer la bille par une autre bille de rayon différent (mais supérieur) de sorte que l'eau initialement versée recouvre exactement cette nouvelle bille
Answered by Claude Tardif.



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