Find $\displaystyle \frac {dy} {dx}$ by implicit differentiation.

$\displaystyle

\tan \frac {x} {y}=x+y

$

By the chain rule, the left side becomes

$\displaystyle \sec^2 (\frac {x} {y}) *$ (the derivative of $\displaystyle \frac {x} {y}$)

I have two problems, one, where do the $\displaystyle y$-primes go, and two, how do I solve for it?

The final answer should look like

$\displaystyle y'= \frac {y \sec^2 \frac {x} {y} - y^2} {y^2 + x \sec^2 \frac {x} {y}}$