Find the derivative using logarithmic differentiation method $3^{\left(2x+1\right)}=3^{\left(8x-3\right)}$

Find the derivative

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

Find the derivative

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

Find the derivative

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

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

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

Find the derivative

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