Question

Solve $\frac{d}{dt}\sqrt{\cos 2t}$

Answer 1

Let us consider the problem:

$\frac{d}{dx}\sqrt{coy2x}$

$=$ $\frac{1}{2}{\cot }^{\frac{1}{2}-1}\left(2x\right)\frac{d}{dx}\left[\cot \left(2x\right)\right]$

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

$=$ $\frac{-2\frac{d^{\left[x\right]}}{dx}\cos e{s}^2\left(2x\right)}{2\sqrt{\cot \left(2x\right)}}$

$=$ $\frac{-1\cos e{s}^2\left(2x\right)}{\sqrt{\cot \left(2x\right)}}$

$=$ $\frac{-\cos e{s}^2\left(2x\right)}{\sqrt{\cot \left(2x\right)}}$