Prove the trigonometric identity $\cos\left(x\right)\cot\left(x\right)=\frac{1}{\sin\left(x\right)}-\sin\left(x\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{3\left(1-\sin\left(x\right)\right)}{2\cos\left(x\right)}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{x^2\sqrt{3x-2}}{\left(x-1\right)^2}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{x^3}{\sin\left(x\right)}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{\frac{\frac{\sqrt{2+x^{22}+x^2 x^2}}{x^2}}{\sqrt{2+x^{22}+x^2 x^2}}}{x^2 x^2}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{2x^3\cdot \cot\left(x^2\right)}{1+e^{2x}}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{e^{\left(x+y\right)}}{2y-1\cdot e^{\left(x+y\right)}}\right)$

Find the derivative

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