$\frac{dy}{dx}=1+\left(\frac{1}{\left(x-y\right)^2}\right)$

$5\sin\left(2x\right)=3\sin\left(x\right)$

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

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

$\lim_{n\to\infty}\left(\frac{\cos\left(n\pi\right)}{2^n}\right)$

$d\left(3x+\frac{1}{\sqrt[3]{x^2}}\right)$

$\frac{2x^3+14x^2-30}{2x-2}$