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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

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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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