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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,

$\frac{1}{x^{2}+y^{2}}\left(2 x+2 y \frac{d y}{d x}\right)=0$

$\frac{d y}{d x}=\frac{-x}{y}$

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