Question:
If $y=\sin ^{-1}(\sin x),-\frac{\pi}{2} \leq x \leq \frac{\pi}{2} .$ Then write the value of $\frac{d y}{d x}$ for $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
Solution:
For $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
$y=\sin ^{-1}(\sin x)$
$=x$
So, $\frac{d y}{d x}=1$ (Ans)
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