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provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 22

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Answer: \cos (\log \sin x) \cdot \cot x

Hint: You must know the rules of solving derivative of trigonometric and logarithm function.

Given:  \sin (\log \sin x)

Solution:

Let  y=\sin (\log \sin x)

Differentiating with respect to x

\frac{d y}{d x}=\frac{d}{d x} \sin (\log \sin x)

Using chain rule

\begin{aligned} &\frac{d y}{d x}=\cos (\log \sin x) \frac{d}{d x}(\log \sin x) \\ &\frac{d y}{d x}=\cos (\log \sin x) \cdot \frac{1}{\sin x} \frac{d}{d x}(\sin x) \end{aligned}

\frac{d y}{d x}=\cos (\log \sin x) \cdot \frac{1}{\sin x} \cdot \cos x

\frac{d y}{d x}=\cos (\log \sin x) \cdot \cot x

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