Derivative of `sec^(-1)((1)/(1-2x^(2)))` w.r.t. `sin^(-1)(3x-4x^(3))` is

Options

A. `(1)/(4)`
B. `(pi)/(6)`
C. `(pi)/(2)`
D. `(pi)/(2)`

Answer

D

Explanation

Let `u = sec^(-1)((1)/(1-2x^(2)))`
`v = sin^(-1)(3x -4x^(3))`
Put `x = sin theta, ` we get
`u = sec^(-1) (sec 2theta), v = sin^(-1)(sin 3 theta)`
`rArr u = 2theta , v = 3 theta`
`rArr u = 2 sin^(1-) x, v = 3 sin^(-1)x`
`rArr (u)/(v) = (2)/(3) rArr u = (2)/(3)v rArr (du)/(dv) = (2)/(3)`