$\left(5a^2b^3\right)\left(6a^3b\right)$

$-15\:-\:\left(-31\right)+\:\left(-82\right)\:-\:\left(3\right)\:+\:\left(-3\right)$

$\frac{dy}{dx}=\frac{4-2x}{3+2y}$

$\log\left(2x\right)=\log\left(32x\right)$

$\lim_{x\to0}\left(\frac{sin\left(3x\right)^2}{x^2\cdot cos\left(5x^3\right)}\right)$

$\frac{d}{dx}x^2+4xy+y^2=1$

$\frac{3x}{x+2}\ge3$