$\frac{dy}{dx}=\frac{xy\left(4-y\right)}{1+x}$

$4z^2-2y^2-8z$

$\int\frac{2}{\left(2+x^{2}\right)}dx$

$\int2x\left(x^2+16\right)^{-15}dx$

$5bc-25cd+50b^4c^2d^2$

$\frac{d^2}{dx^2}\left(e^{-x}\cos\left(y\right)-e^{-y}\cos\left(x\right)\right)$

$\int\frac{\left(x^2+x^{\frac{1}{2}}\right)}{x^{\frac{1}{3}}}dx$