Question

Differentiate

$\sqrt{a^{2}co{s}^{2}x+b^{2}si{n}^{2}x}$

Answer 1

Given, $y=\sqrt{a^2{\cos }^{2}x+b^2{\sin }^{2}x}$

Differentiate on both sides w.r.t x

$\frac{dy}{dx}=\frac{1}{2\sqrt{a^2{\cos }^{2}x+b^2{\sin }^{2}x}}\frac{d}{dx}(a^2{\cos }^{2}x+b^2{\sin }^{2}x)$

$=\frac{-2a^2\cos x\sin x+2b^2\sin x\cos x}{2\sqrt{a^2{\cos }^{2}x+b^2{\sin }^{2}x}}$

$\therefore \frac{dy}{dx}=\frac{(b^2-a^2)\sin x\cos x}{\sqrt{a^2{\cos }^{2}x+b^2{\sin }^{2}x}}$