Question

If `y = tan^-1((sqrtx - x)/(1 + x^{3/2}))`, then y'(1) is ______ 

विकल्प

• 0

• `1/2`

• -1

• `-1/4`

Answer 1

If `y = tan^-1((sqrtx - x)/(1 + x^{3/2}))`, then y'(1) is `underline(-1/4)`.

Explanation:

`y = tan^-1((sqrtx - x)/(1 + x^{3/2})) = tan^-1(sqrtx) - tan^-1(x)`

∴ `y^' = 1/(1 + x). 1/(2sqrtx) - 1/(1 + x^2)`

∴ `y^'(1) = 1/2. 1/2 - 1/2 = (-1)/4`