$\lim_{x\to0}\left(\frac{e^{5x\:}-1}{\sin\left(x\right)}\right)$

$\frac{dy}{dx}\left(x^2-y^2=36\right)$

$f\left(x\right)=\frac{\left(3x-6\right)^{3}}{\left(6x+3\right)^{4}}$

$\lim_{x\to0}\left(\frac{3sin\left(8x^6\right)}{4x}\right)$

$\frac{d}{dx}\sqrt{1-t}$

$\frac{dy}{dx}=\frac{4xy^2}{y^2-1}$

$\lim_{x\to\infty}\left(\frac{1}{2}\ln\left(\frac{x+1}{\sqrt{x^2+1}}\right)\right)$