Quandaries
and Queries 

Name: Emily I am: A student Grade Level: 12th grade Hello :) I am confused with what I am suppose to do for the following problem... If x^3+3xy+2y^3=17, then in terms of x and y, dy/dx = a. (x^2+y/x+2y^2) b. (x^2+y/x+y^2) c. (x^2+y/x+2y) d. (x^2+y/2y^2) e. (x^2)/(1+2y^2) I'm not sure what to do, but here is what I have so far. Let me know if I am on the right track and what I should do. x^3+[3(1)+y(3)]+(6y^2)=0 3x^2+3x+3y+6y^2 = x^2+x+y+2y^2 Thank you! ~Emily 

Hi Emily, In this problem you need to keep in mind that y is a function of x, that is y is just the name for some expression in x that you don't know. It might be that y = x^{3} + 4 or y = x^{2} + 1, you don't know. Hence, when you have to find the derivative of y you can't calculate it, all you can say is that it is the derivative of y with respect to x, that is dy/dx. In particular part of your expression is 3xy and you have to differentiate this. It is a product so you need to use the product rule. So differentiating 3xy I get
the derivative of x is 1 so this is
The derivative of y you can't calculate so the best you can get is
Likewise with the term 2y^{3}. The derivative is
Thus with the expression
when you differentiate both sides with respect to x you get
Now solve foy dy/dx. Penny 

