Find the limit of $\frac{\left(2x+3\right)\sqrt{x-1}}{2x^2+x-3}$ as $x$ approaches $1$

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

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