Provide Solution For  R.D.Sharma Maths Class 12 Chapter 10 Differentiation Exercise 10.3 Question 40 Maths Textbook Solution.

Answer: $\frac{dy}{dx}=0$

Hint:

$\frac{\mathrm{d}}{\mathrm{d} \mathrm{x}}\left(\mathrm{x}^{\mathrm{n}}\right)=\mathrm{n} \mathrm{x}^{\mathrm{n}-1} ; \frac{d}{\mathrm{dx}}(\text { constant })=0$

Given:

$y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right) x>0$

Solution:

\begin{aligned} &\mathrm{y}=\sec ^{-1}\left(\frac{\mathrm{x}+1}{\mathrm{x}-1}\right)+\sin ^{-1}\left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right) \mathrm{x}>0 \\ &\mathrm{y}=\cos ^{-1}\left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right)+\sin ^{-1}\left(\frac{\mathrm{x}-1}{\mathrm{x}+1}\right) \end{aligned}

Using $\sec ^{-1}x=\cos \left ( \frac{1}{x} \right )$

Since,$\cos ^{-1}x+\sin ^{-1}x=\frac{\pi}{2}$

$y=\frac{\pi}{2}$

Differentiating with respect to $x$

$\frac{dy}{dx}=0$                                                                                                $\left [ \frac{d }{dx} \left ( constant \right )=a]\right ]$