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need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 34

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Answer:  \frac{2 e^{\sin ^{-1} 2 x}}{\sqrt{1-4 x^{2}}}

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

Given: e^{\sin ^{-1} 2 x}

Solution:

Let  y=e^{\sin ^{-1} 2 x}

Differentiate with respect to x,

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left[e^{\sin ^{-1} 2 x}\right] \\\\ &\frac{d y}{d x}=e^{\sin ^{-1} 2 x} \times \frac{d}{d x}\left(\sin ^{-1} 2 x\right) \end{aligned}

\begin{aligned} &\frac{d y}{d x}=e^{\sin ^{-1} 2 x} \times \frac{1}{\sqrt{1-(2 x)^{2}}} \frac{d}{d x}(2 x) \\\\ &\frac{d y}{d x}=\frac{2 e^{\sin ^{-1} 2 x}}{\sqrt{1-4 x^{2}}} \end{aligned}

 

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