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Explain solution RD Sharma class 12 chapter 9 Differentiability exercise Fill in the blanks question  4 maths

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Answer: \pm \pi hence there are 2 points where f(x) is not differentiable

Hint: : If f(x) is differentiable at all x\in R, we must showf'(x)exists at all x\in R

Given: The function f(x)=\sin ^{-1}(\sin x) is not differentiable is


f(x)=\sin ^{-1}(\sin x)

The function f(x)is continuous everywhere but not differentiable at (2 n+1) \frac{\pi}{2}, n \in Z

f(x) is an odd function.

f^{\prime}(x)=(-1)^{n} \text {, if }(2 n-1) \frac{\pi}{2}<x<(2 n+1) \frac{\pi}{2}

\therefore x=\pm \pi where f(x) is not differentiable

\therefore hence there are 2 points where f(x)  is not differentiable


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