Question

Differential coefficient of `sin^-1(sqrtx)` with respect to `sqrt(1 - x)` is ______ 

Options

• `sqrtx`

• `-sqrtx`

• `1/sqrtx`

• `-1/sqrtx`

Answer 1

Differential coefficient of `sin^-1(sqrtx)` with respect to `sqrt(1 - x)` is `underline(-1/sqrtx)`.

Explanation:

Let `y = sin^-1(sqrtx)` and `z = sqrt(1 - x)` 

∴ `dy/dx = 1/(sqrt(1 - x)) . 1/(2sqrtx)` and `dz/dx = (-1)/(2sqrt(1 - x))`

∴ `dy/dz = (dy/dx)/(dz/dx) = (-1)/sqrtx`