$\lim_{x\to-\infty\:}\left(\frac{\left(\sqrt[2]{2x^2+1}\right)}{4x+2}\right)$

$\frac{d}{dx}\left(\frac{\left(x\sqrt{x^5+6}\right)}{\left(x+8\right)^{\frac{2}{3}}}\right)$

$\lim_{x\to0}\left(\frac{e^x}{xe^x}\right)$

$\left(\frac{1}{2}x^4-\frac{2}{3}y\right)^3$

$\frac{d}{dx}3x^2y\:-\:xy\:=\:46\:+\:y\:$

$\frac{d}{dx}xy^2+x^2y$

$\frac{dx}{dz}=\frac{x^3}{z^2}$