(\frac{d}{dx}\left(tan^{-1}\left(\frac{\sqrt{x}-\sqrt{a}}{1+... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

$\frac{d}{dx}\left(tan^{-1}\left(\frac{\sqrt{x}-\sqrt{a}}{1+\sqrt{xa}}\right)\right)$ , $x$ , $a > 0$ , is

A

$tan^{-1}\sqrt{x}+tan^{-1}\sqrt{a}$

B

$\frac{1}{1+x}$

C

$\frac{1}{1+x}+\frac{1}{1+a}$

D

$\frac{1}{2\sqrt{x}\left(1+x\right)}$

Answer

$\frac{1}{2\sqrt{x}\left(1+x\right)}$

Explanation

Solution

Answer (d) $\frac{1}{2\sqrt{x}\left(1+x\right)}$