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

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

Answers (1)

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)

Solution:

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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