$\frac{dy}{dx}\left(\frac{4x^2\:+\:x^3}{x^4\:+\:1}\right)$

$4x+3^2$

$=\frac{1}{\csc\left(x\right)\cdot\cot\left(x\right)}$

$\left(xy+x\right)dx\:+\:\left(x^2y^2+x^2+y^2+1\right)dy=0$

$\frac{25x^2}{4}+\frac{20xy}{3}+\frac{2y^2}{3}$

$\left(4-5+12-9\right)+3-2-\left(7-17+12\right)-5$

$3x^2+8xy^2-10x^2y+2xy+7x^2y$