Question

Solve

$\frac{d}{dx}[\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}{\sin }^{-1}\frac{x}{a}]=$

Answer 1

Let $y=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}si{n}^{-1}\frac{x}{a}$

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

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

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