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

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

Answers (1)

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 ]

 

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