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Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 36 maths textbook solution

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Answer:  \frac{e^{\tan ^{-1 \sqrt{x}}}}{2 \sqrt{x}(1+x)}

Hint: You must know about the rules of solving derivative of Exponential and Inverse trigonometric function.

Given: e^{\tan ^{-1} \sqrt{x}}


Let  y=e^{\tan ^{-1} \sqrt{x}}

Differentiate with respect to x,

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left[e^{\tan ^{-1} \sqrt{x}}\right] \\\\ &\frac{d y}{d x}=e^{\tan ^{-1} \sqrt{x}} \frac{d}{d x}\left(\tan ^{-1} \sqrt{x}\right) \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\frac{e^{\tan ^{-1} \sqrt{x}}}{1+x} \times \frac{1}{2 \sqrt{x}}\\\\ &\frac{d y}{d x}=\frac{e^{\tan ^{-1 \sqrt{x}}}}{2 \sqrt{x}(1+x)} \end{aligned}

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