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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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