$\frac{d}{dx}\left(1+2\ln\left(x\right)\right)^x$

$\frac{6}{x^{\frac{1}{2}}}-\frac{15}{x^{\frac{4}{5}}}$

$5x+\frac{3}{10}y+2x+\frac{29}{40}y$

$\frac{x^3+x}{\:\sqrt{1+x^2}}$

$\frac{x^3+6x-2}{x-1}$

$\int x^{13}\left(x^7-5\right)^{\frac{3}{2}}dx$

$\frac{dy}{dx}\:-5y\:+5xy^3\:=\:0$