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need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 27

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Answer: \cos x \sec ^{2}\left(e^{\sin x}\right) e^{\sin x}

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

Given: \tan \left(e^{\sin x}\right)


Let  y=\tan \left(e^{\sin x}\right)

Differentiate with respect to x

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left[\tan \left(e^{\sin x}\right)\right] \\ &\frac{d y}{d x}=\sec ^{2}\left(e^{\sin x}\right) \frac{d}{d x}\left(e^{\sin x}\right) \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\sec ^{2}\left(e^{\sin x}\right) \times e^{\sin x} \frac{d}{d x}(\sin x) \\ &\frac{d y}{d x}=\cos x \cdot \sec ^{2}\left(e^{\sin x}\right) \cdot e^{\sin x} \end{aligned}

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