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differentiation

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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?
Thanks.

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.
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.
The derivative of y = sin (30 + x) 2012-11-07
From Saskia:
derivative of y = sin (30 + 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.
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.
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 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.
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.
Implicit differentiation 2009-02-18
From Sunny:
Find slope of the tangent line to the curve 2(x^2+y^2)2=25(x^2y^2) at (3,-1)
Answered by Robert Dawson and 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.
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)=[(2x)(2x^2)-(x^2-4)(4x)]/[(2x^2)^2]
f''(x)=[(4x^3-(4x^3 -16x)]/4x^4
f''(x)=16x/4x^4
f''(x)=4/x^3

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

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.
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 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.
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.
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.
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

x^lnx

x^(e^(-x^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.
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.
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.
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.
A partial derivative 2004-03-19
From Penny Nom:
Is it possible to differentiate the following equation, if so could you please explain.

S=SQRT(T-(5/X^2))

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.
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.
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.
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 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.
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.
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 :

y-c/p=xp^2-cp^3
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.
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.

 
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