Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(x^{\frac{1}{x}}\right)$

Find the derivative

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

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

$\frac{d}{dx}\left(\frac{2x^3}{\left(2-5x\right)\sqrt{x^2+1}}\right)$

Find the derivative

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

Find the derivative

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