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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
If $y=\sin ^{-1} x$ then find $\frac{d^2 y}{d x^2}$.
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Answer

$\begin{aligned} y & =\sin ^{-1} x \\ \frac{d y}{d x} & =\frac{1}{\sqrt{1-x^2}} \\ \text { and } \quad \frac{d^2 y}{d x^2} & =\left(-\frac{1}{2}\right)\left(1-x^2\right)^{-3 / 2}(0-2 x) \\ & =\frac{x}{\left(1-x^2\right) \sqrt{1-x^2}}\end{aligned}$

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