Question:
Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ in each of the following:
$\tan ^{-1}\left(x^{2}+y^{2}\right)=a$
Solution:
We are given with an equation $\tan ^{-1}\left(x^{2}+y^{2}\right)=a$, we have to find $\frac{d y}{d x}$ of it, so by differentiating the equation on both sides with respect to $x$, we get,
$\frac{1}{x^{2}+y^{2}}\left(2 x+2 y \frac{d y}{d x}\right)=0$
$\frac{d y}{d x}=\frac{-x}{y}$