Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The derivative of cos-1(2x2 - 1) w.r.t. cos-1 x A. 2

The derivative of \cos ^{-1}\left(2 x^{2}-1\right) w.r.t \cos ^{-1} x is

\\A \ 2 \\B \ \frac{-1}{2 \sqrt{1-\mathrm{x}^{2}}} \\\\C \ \frac{2}{x} \\ \\D. 1-x^{2}

Answers (1)

A)

\\ \text { Let } u=\cos ^{-1}\left(2 x^{2}-1\right) \text { and } v=\cos ^{-1} x \\ \text { Now, } u=\cos ^{-1}\left(2 x^{2}-1\right) \\ u=\cos ^{-1}\left(2 \cos ^{2} v-1\right)\left[\cdot v=\cos ^{-1} x\rightarrow \cos v=x\right] \\ u=\cos ^{-1}(\cos 2 v)\left[\because 2 \cos ^{2} x-1=\cos 2 x\right] \\ \Rightarrow u=2 v \\ \quad \frac{d u}{d v}=2

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question