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The derivative of cos^(-1)(2x^(2)-1) w.r...

The derivative of `cos^(-1)(2x^(2)-1)` w.r.t. `cos^(-1)` is

A

`2`

B

`(-1)/(2sqrt(1-x^(2)))`

C

`2/x`

D

`1-x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `u =cos^(-1)(2x^(2)-1)` and `v = cos^(-1)x`
`:. (dv)/(dx)=("+-"1)/(sqrt(1-(2x^(2)-1)^(2))).4x = (-4x)/(sqrt(1-(4x^(4)+1-4x^(2))))`
`= (-4x)/(sqrt(-4x^(4)+4x^(2)))=(-4x)/(sqrt(4x^(2)(1-x^(2))))`
`= (-2)/(sqrt(1-x^(2)))`
and `(du)/(dx) = (-1)/(sqrt(1-x^(2)))`
`:. (dx)/(dv) = (du//dx)/(dv//dx) = (-2//sqrt(1-x^(2)))/(-1//sqrt(1-x^(2))) = 2`
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