$\lim_{x\to\infty}\left(\frac{t^{\frac{2}{3}}}{1}\right)$

$\left(2xy^2-3\right)\left(4x^2y^4+6xy^2+9\right)$

$\frac{d}{dx}\left(\frac{\left(x-2\right)\left(x+4\right)}{\left(x-1\right)\left(x+3\right)}\right)$

$\frac{dy}{dx}\left(5xy-7y^2=5\right)$

$\frac{2x^2+17x+16}{x+7}$

$y^2+2y^2-4y-8$

$\frac{dy}{dx}=y\left(xy^3-2\right)$