Differentiate ^2 ( ^ −1 (x^2)) w.r. to x - Vidyadip

Question

Differentiate $\sin^2 (\sin^{−1}(x^2))$ w.r. to $x$

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Answer

$ \text { Let } y=\sin ^2\left[\sin ^{-1}\left(x^2\right)\right]$
$=\left[\sin \left\{\sin ^{-1}\left(x^2\right)\right\}\right]^2$
$=\left(x^2\right)^2$
$\therefore y=x^4 $
Differentiating w. r. t. x, we get
$\frac{ d y}{ d x}=\frac{ d }{ d x}\left(x^4\right)=4 x ^3$

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