# Homework Help: Implicit Differentiation Help

1. Jul 11, 2012

### communitycoll

1. The problem statement, all variables and given/known data
Find dy / dx for sqrt(xy) = x - 2y.

2. Relevant equations

I don't know how to simplify

[(xy' + y) / 2sqrt(xy)] = (1 - 2y')

to

y' = [- y + 2sqrt(xy)] / [x + 4sqrt(xy)].

3. The attempt at a solution

I do everything Wolfram Alpha does here:

http://www.wolframalpha.com/input/?i=derivative+sqrt(xy)+=+x+-+2y

and at the end of the steps shown above, I want to multiply (1 - 2y') by 2sqrt(xy), to get

2sqrt(xy) - 4y'sqrt(xy)

although I don't think that's correct.

I just realized all I d is solve for y' (didn't occur to me for some reason), and now need to know if I plug in the original equation into all of the y values (I think I remember seeing my prof. do this in class). Ayuda me por favor.

Last edited by a moderator: Jul 12, 2012
2. Jul 11, 2012

### eumyang

Yes, that's correct. Now rearrange the terms so that the ones with y' are on one side, and the other terms are on the other. Solve for y'.

EDIT: It looks like you figured it out already.

3. Jul 12, 2012

### communitycoll

Thanks. I appreciate it.