Differentiate the following w. r. t. x. ^2 ( ^ -1 (x^2 ) ) - Vidyadip

Question

Differentiate the following w. r. t. x.$\sin ^2\left(\sin ^{-1}\left(x^2\right)\right)$

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Answer

$
\begin{aligned}
& \text { (vi) Let } y=\sin ^2\left(\sin ^{-1}\left(x^2\right)\right) \\
& =\left[\sin \left(\sin ^{-1}\left(x^2\right)\right]^2=\left(x^2\right)^2\right. \\
& \therefore \quad y=x^4 \\
&
\end{aligned}
$
Differentiate w.r.t.x.
$
\frac{d y}{d x}=\frac{d}{d x}\left(x^4\right) \quad \therefore \frac{d y}{d x}=4 x^3
$

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