$\frac{dy}{dx}=\ln\left(x\right)+4x$

$\frac{y^2+1}{y+1}$

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

$x^2\frac{dy}{dx}=\left(y+1\right)^2\left(x+1\right)$

$10xy-2y-x-3xy-2y-x$

$\lim\:_{n\to\:\infty\:\:\:\:}\left(\frac{7n^{\frac{3}{2}}}{7n^{\frac{3}{2}}-10n+2}\right)$