$\lim_{x\to\infty}\left(-\frac{2\cdot ln\left(2^x-1\right)}{x+1}\right)$

$\frac{dy}{dx}=\frac{\left(5x^2+3x\right)}{y^2}$

$x^2+11x+56$

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

$500-5y-y^2>220$

$\:f\left(x\right)=\left(9-8x^2\right)\left(-2-5x+10x^3\right)$

$-2x^3-5x^3-2x^3$