Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\left(x^2+4\right)^{\left(3x-1\right)}\right)$

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^6+2\right)^x$

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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