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Please solve RD Sharma class 12 chapter Differentiation exercise 10.8 question 21 maths textbook solution

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Answer: -2 e^{-\cos x} \cos x

Hint: \text { let } u=\sin ^{2} x, v=e^{\cos x}

Given: \sin ^{2} x \text { w.r.t } e^{\cos x}



u=\sin ^{2} x

\begin{aligned} &\frac{d u}{d x}=2 \sin x \cos x \\\\ &v=e^{\cos x} \\\\ &\frac{d v}{d x}=e^{\cos x}(-\sin x)=-\sin x e^{\cos x} \end{aligned}

\frac{d u}{d v}=\frac{\frac{d u}{d x}}{\frac{d v}{d x}}=\frac{2 \sin x \cos x}{-\sin x e^{\cos x}}=-2 \cos x e^{-\cos x}



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