Question

Differentiate the following w.r.t x : $\frac{\sqrt{a^2-x^2}}{x^2}$

Answer 1

$\frac{d}{dx}\frac{\sqrt{a^2-x^2}}{x^2}$

$=\frac{x^2\frac{d}{dx}\left(\sqrt{a^2-x^2}\right)-\frac{d}{dx}\left(x^2\right)\sqrt{a^2-x^2}}{(x^2{)}^2}$

$\frac{d}{dx}\left(\sqrt{a^2-x^2}\right)=-\frac{x}{\sqrt{a^2-x^2}}$

$\frac{d}{dx}\left(x^2\right)=2x$

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

$=\frac{x^2-2a^2}{x^3\sqrt{a^2-x^2}}$