Find the limit of $\frac{\ln\left(x^4\right)}{x^3}$ as $x$ approaches $\infty $

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d}{dx}\sqrt{x}$

Find the derivative

$\frac{d}{dy}\left(y^{\left(-1\right)\cdot\frac{1}{2}}\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^{\frac{1}{4}}\right)$

Evaluate the limit

$\lim_{x\to\infty}\left(\frac{\sqrt{2x}+\sqrt{x}+\sqrt{x}}{\sqrt{x\sqrt{x}\sqrt{x}}}\right)$