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Please solve RD Sharma class 12 chapter 10 Differentiation exercise Fill in the blanks question  17 maths textbook solution

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Answer: \frac{d y}{d x}=0

Hint: \frac{d}{d x}=\left(\sin ^{-1} x\right)=\frac{1}{\sqrt{1-x^{2}}}

Given: y=\sin ^{-1}\left(e^{x}\right)+\cos ^{-1}\left(e^{x}\right)

Solution:  y=\sin ^{-1}\left(e^{x}\right)+\cos ^{-1}\left(e^{x}\right)

Differentiating (i) we get;

\begin{aligned} \frac{d y}{d x} &=\frac{1}{\sqrt{1+e^{2x}}} e^{x}-\frac{1}{\sqrt{1+e^{2x}}} e^{x} \\\\ &=0 \end{aligned}

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