Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(x^{\left(x-3\right)}\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x-1\right)^{\cos\left(2x\right)}$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(1+\frac{1}{x}\right)^x$

Find the derivative

$\frac{d}{dx}\left(1+\frac{7}{x}\right)^x$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^{x+1}\right)$