AP Calc help

Test Preparation AP Mathematics & Computer Science
1

I am having trouble with these two question for derivative type questions. Can someone help me with these and explain how to do them. Thanks in advance

  1. Find DY/DX at x=2 if y=6u^2 -11 and u=3x^2 + 2
  2. use implicit differentiation to find DY/DX for xy^2 - yx^2 = 3xy. Note that for question two there are no brackets so the squared only go to the y for xy^2 and for the x for yx^2.
2

@zxcvbnm1216 For 1, replace u with 3x^2 + 2 in the equation for y. Shouldn’t be too hard.

For 2, please read on implicit differentiation first (as this is a fairly straightforward question). Remember that if you take the derivative of both sides with respect to x, then because y is a function of x, you have to use the chain rule every time a y is involved. For example:

If y^2 = x + 5, then differentiating both sides w.r.t. x gives 2y (dy/dx) = 1, or dy/dx = 1/2y.

Remember that CC is not supposed to be a homework help site, and because I want you to actually learn how to solve the problems, it wouldn’t benefit either of us for me to give you the full solution.

3

thanks @MITer94

4

for 1 would it be:
@MITer94
du/dx = 6x
dy/du = 12u

dy/dx = dy/du * du/dx
dy/dx = 12u * 6x
dy/dx = 6x(36x^2 + 24)
dy/dx = 216x^3 + 144x
@ x=2
dy/dx = 2016

5

@zxcvbnm1216 that seems correct. Alternatively:

y = 6(3x^2 + 2)^2 - 11
= 54x^4 + 72x^2 + 13
==> dy/dx = 216x^3 + 144x

6

thanks so much @MITer94