$\lim_{x\to0}\left(\frac{\sqrt{6+x}-3}{x}\right)$

$5x^3y-20x^2y^2-100xy$

$\frac{d^2}{dx^2}\left(cos\left(3x^2+3\right)\right)$

$\frac{d}{dx}2\sqrt{x^3}+3\sqrt{x}$

$\left(3x^2-x+5\right)\left(x^2+3x-9\right)$

$\int_0^{\infty}\left(y^3e^{-y^2}\right)dx$

$\frac{1}{sec^2\left(t\right)-1}$