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

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

Answers (1)

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}}

Solution:

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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