Prove the trigonometric identity $\frac{1+\sin\left(\theta\right)}{\cos\left(\theta\right)}+\frac{\cos\left(\theta\right)}{1+\sin\left(\theta\right)}=2\sec\left(\theta\right)$

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

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

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

$\frac{d}{dx}\left(x\arctan\left(x\right)\right)$

$\frac{d}{dx}\left(\mathrm{sech}\left(-4x\right)\left(1-\ln\left(\mathrm{sech}\left(-4x\right)\right)\right)\right)$

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

$\frac{d}{dx}\tan\left(x\right)$