$\cot\left(x\right)=\cos\left(x\right)\sin\left(x\right)+\cos\left(x\right)\csc\left(x\right)$

$\frac{dy}{dx}=12-\frac{y}{100+2x}$

$3x+\frac{x}{2}$

$\lim_{x\to\frac{\pi}{2}}\left(\frac{5secx}{4tanx+4}\right)$

$\frac{\left(x-2\right)}{x^2-1}\:+\:\frac{\left(x-1\right)}{x+1}$

$\lim_{x\to0}\left(\frac{ln\left(sin\left(x\right)\right)}{ln\left(tan\left(3x\right)\right)}\right)$

$\lim_{x,y\to0,0}\left(\frac{xy^3}{x^2+y^6}\right)$