$\frac{dy}{dx}=\frac{x+y+1}{x+y-2}$

$-80r^6+14t^2-102t^2r^3$

$2sin^2x\:+3sinx\:=\:-1$

$\lim_{x\to\infty}\left(\frac{x+1}{k}\right)$

$8y+\left(-4x\right)-5x+1-6y+2$

$\frac{d}{dx}\left(y=\left(4x\right)^{ln\left(4x\right)}\right)$

$\left(4xy^2+6\right)\left(4xy^2-\frac{3}{4}\right)$