Question

Find dy/dx of sqrt(x+y) + sqrt(xy) = 6

Answer 1

=\[sqrt{xy}\/\(sqrt{x+y}\=sqrt{xy}\)\]

Answer 2

if this is the ans..i will explain...let me know..

Answer 3

what are the red dashes for? and sorry i do not know the answer of this problem.

Answer 4

=\[sqrt{xy}\/\(sqrt{x+y}\+sqrt{xy}\)\]

red was f0r eqstn editor...it didint worked...

Answer 5

uh maybe type in normal horizontal equation please :)

Answer 6

\[\frac{d}{dx}[\sqrt{x+y} + \sqrt{xy}] = 0\]\[\implies \frac{d}{dx}[\sqrt{x+y}] + \frac{d}{dx}[\sqrt{xy}] = 0\]By the chain rule:\[\implies \frac{1}{2\sqrt{x+y}}\cdot \frac{d}{dx}[x+y] + \frac{1}{2\sqrt{xy}}\cdot \frac{d}{dx}[xy] = 0\]\[\implies \frac{1}{2\sqrt{x+y}}(1 + \frac{dy}{dx}) + \frac{1}{2\sqrt{xy}}\cdot (x\frac{dy}{dx} + y) = 0\]

And continue from there to solve for \(\frac{dy}{dx}\)

Answer 7

I gotta run to the store, but if you get stuck, lemme know.

Answer 8

you refer to dy/dx is just like y' right? 'cause i used y' it's cleaner haha. but that's an awesome and very clean looking solution. thanks a lot. +1