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The derivative of sin^(-1) (2x sqrt(1-x...

The derivative of ` sin^(-1) (2x sqrt(1-x^(2))) ` with respect to ltbr. ` sin^(-1)(3x - 4x^(3))` is

A

` (2)/(3)`

B

`(3)/(2)`

C

`(1)/(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` y = sin^(-1) (2x sqrt( 1 - x^(2))) " and " z = sin^(-1) (3x - 4x^(3))` ltbr. rArr y = 2 sin^(-1) x "and "z = 3 sin^(-1) x `
` rArr y = (2)/(3) z `
On differentiating both sides w.r.t.x., we get
` (dy)/(dz)=(2)/(3)`
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