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

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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