Q95 / 180 · KCET 2017 · Mathematics

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

  • Correct answer
    A
    \( 12 \)
  • B
    \( -\frac{1}{2 \sqrt{1-x^{2}}} \)
  • C
    \( \frac{2}{x} \)
  • D
    \( 1-x^{2} \)

Solution

Let \( y=\cos ^{-1}\left(2 x^{2} \quad 1\right)=2 \cos ^{-1} x \) and \( z=\cos ^{-1} x \)
So, \( \frac{d y}{d z}=\frac{d\left(2 \cos ^{-1} x\right)}{d \cos ^{-1} \chi}=2 \)

Hence, the correct answer is option: 'A'.

Relevant Questions