Find the derivative using logarithmic differentiation method $\cos\left(\sqrt{4x}\right)+\sqrt{\cos\left(4x\right)}$

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(\left(\left(7^x\right)^{37}\right)^{121\left(-1\right)\cdot x}\right)$

Find the derivative

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