Find the derivative using logarithmic differentiation method $\frac{d^2}{dx^2}\left(\sin\left(4x\right)\right)\cos\left(y\right)$

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

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