Question

Differentiate $x{\cos }^{-1}x$.

Answer 1

$\frac{d}{dx}\left(x{\cos }^{-1}x\right)$

$={\cos }^{-1}x\frac{d}{dx}\left(x\right)+x\frac{d}{dx}\left({\cos }^{-1}x\right)$

$=1\times {\cos }^{-1}x+(-\frac{1}{\sqrt{1-x^2}})x$

$={\cos }^{-1}x-\frac{x}{\sqrt{1-x^2}}$

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