How do I find dy/dx for sqrt(xy) = x - 2y using implicit differentiation?

[communitycoll]

Homework Statement

Find dy / dx for sqrt(xy) = x - 2y.

Homework Equations

I don't know how to simplify

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

to

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

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.

Help please.

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.

 

[eumyang]

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.

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.

 

[communitycoll]

Thanks. I appreciate it.