Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(x^{-2x}\right)$

Find the derivative

$\frac{d}{dx}x^{e^x}$

Find the derivative

$\frac{d}{dx}x^{cosx}$

Find the derivative

$\frac{d}{dx}\left(x^{5\sin\left(x\right)}\right)$

Find the derivative

$\frac{d}{dx}\left(\left(sinx\right)^{cosx}\right)$

Find the derivative

$\frac{d}{dx}\left(cosx^{sinx}\right)$

Find the derivative

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

Find the derivative

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