Implicit differentiation for √(x/y) + √(y/x) = 10

[hoaver]

Homework Statement

Prove that
$$\frac{dy}{dx}=\frac{y}{x}$$
for
$$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=10$$
x is not equal to y which is not equal to 0

The Attempt at a Solution

Tried all the normal methods but none seem to work...anyone have any ideas?

 

[gabbagabbahey]

The Attempt at a Solution

Tried all the normal methods but none seem to work...anyone have any ideas?

Really?...show us!