Question
Differentiate the following w. r. t. x.$\sin ^{-1}\left(x^3\right)$
✓
Answer
Let $y=\sin ^{-1}\left(x^3\right)$
Differentiate $w . r . t . x$.
$
\begin{aligned}
\frac{d y}{d x} & =\frac{d}{d x}\left(\sin ^{-1}\left(x^3\right)\right) \\
& =\frac{1}{\sqrt{1-\left(x^3\right)^2}} \cdot \frac{d}{d x}\left(x^3\right) \\
& =\frac{1}{\sqrt{1-x^6}}\left(3 x^2\right) \\
\therefore \quad \frac{d y}{d x} & =\frac{3 x^2}{\sqrt{1-x^6}}
\end{aligned}
$
Differentiate $w . r . t . x$.
$
\begin{aligned}
\frac{d y}{d x} & =\frac{d}{d x}\left(\sin ^{-1}\left(x^3\right)\right) \\
& =\frac{1}{\sqrt{1-\left(x^3\right)^2}} \cdot \frac{d}{d x}\left(x^3\right) \\
& =\frac{1}{\sqrt{1-x^6}}\left(3 x^2\right) \\
\therefore \quad \frac{d y}{d x} & =\frac{3 x^2}{\sqrt{1-x^6}}
\end{aligned}
$
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