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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 13 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.5 question 13 maths textbook solution

Answers (1)

Answer:  \sin x^{x}(\log \sin x+x \cot x)

Hint: Diff equation by \sin ^{x}

Given: \sin x^{x}

Solution:  Let y=(\sin x)^{x}

Taking log on both sides

        \begin{aligned} &y=\sin x^{x} \\\\ &\log y=\log \sin x^{x} \\\\ &\log y=x \log \sin x \\\\ &\frac{1}{y} \frac{d y}{d x}=\log \sin x+x \cot x \\\\ &\frac{d y}{d x}=\sin x^{x}(\log \sin x+x \cot x) \end{aligned}

 

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