Question

Differentiate the following function w.r.t. x: ${\tan }^{-1}\left(\frac{\sqrt{1+a^2{x}^2}-1}{ax}\right)$.

Answer 1

$\frac{\frac{a^3{x}^2}{\sqrt{1+a^2{x}^2}}+a-a.\sqrt{1+a^2{x}^2}}{a^2.x^2(1+(\frac{\sqrt{1+a^2{x}^2}-1}{ax}{)}^2)}$

$\frac{a(\sqrt{1+a^2{x}^2}-1)}{\sqrt{1+a^2{x}^2}(a^2{x}^2+(\sqrt{1+a^2{x}^2}-1{)}^2)}$