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provide solution for RD Sharma maths class 12 chapter Differentiation exercise  10.2 question 18

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Answer: 2(\log \sin x) \cot x

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

Given: (\log \sin x)^{2}


Let  y=(\log \sin x)^{2}

Differentiating with respect to x

\frac{d y}{d x}=\frac{d}{d x}(\log \sin x)^{2}

\frac{d y}{d x}=2(\log \sin x) \frac{d}{d x}(\log \sin x)

\frac{d y}{d x}=2(\log \sin x) \times \frac{1}{\sin x} \frac{d}{d x}(\sin x)

\begin{aligned} &\frac{d y}{d x}=2(\log \sin x) \times \frac{1}{\sin x} \times \cos x \\ &\frac{d y}{d x}=2(\log \sin x) \times \cot x \end{aligned}

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