Question

If y = `cot^-1(x/(sqrt(1 - x^2)))`, then `dy/dx` is equal to ______ 

Options

• `(-1)/sqrt(1 - x^2)`

• `x/sqrt(1 - x^2)`

• `1/sqrt(1 - x^2)`

• `sqrt(1 - x^2)/x`

Answer 1

If y = `cot^-1(x/(sqrt(1 - x^2)))`, then `dy/dx` is equal to `underline((-1)/sqrt(1 - x^2))`.

Explanation:

Put x = cos θ ⇒ θ = `cos^-1x`

∴ `y = cot^-1(costheta/sqrt(1 - cos^2theta))`

= `cot^-1(costheta/sintheta)`

= `tan^-1(tantheta)`

= θ = cos^-1x 

∴ `dy/dx = (-1)/sqrt(1 - x^2)`