Question

`d/dx[cot^-1(sqrtx)]` = ______ 

विकल्प

• cosec^-1 x

• `(-1)/(2sqrtx(1 + x))`

• `(-1)/(1 + x)`

• `(2sqrtx)/(1 + x)`

Answer 1

`d/dx[cot^-1(sqrtx)]` = `underline((-1)/(2sqrtx(1 + x)))` 

Explanation:

`d/dx[cot^-1(sqrtx)] = (-1)/(1 + (sqrtx)^2) . 1/(2sqrtx) = (-1)/(2sqrtx(1 + x))`