$\frac{dz}{dr}x^2-xr^2-1=0$

$\frac{dy}{dx}=e^2^x\cos y$

$\lim_{x\to-2}\left(\frac{4\:cos\:\left(x+2\right)-x^2}{4e^{-4-2x}-x^2}\right)$

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

$\tan\left(45+x\right)=\frac{\cos\left(x\right)+\sin\left(x\right)}{\cos\left(x\right)-\sin\left(x\right)}$

$\frac{d}{dx}\left(y=5ln\left(3lnx\right)\right)$

$\frac{dx}{dt}-\frac{2x}{t}=\ln\left(t\right)$