Manipulaciones diferenciales

$$d(x+y)=dx + dy$$

$$d(xy)=ydx + xdy$$

$$d\left( \frac{x}{y}\right)= \frac{ydx-xdy}{y^2}$$

$$d\left( \frac{y}{x}\right)= \frac{xdy-ydx}{x^2}$$

$$d\left( \frac{x^2}{y}\right)= \frac{2xydx-x^2dy}{y^2}$$

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

$$d\left(arctan \frac{y}{x}\right)= \frac{xdy-ydx}{x^2+y^2}$$

$$d\left(\frac{1}{2}ln \: (x^2+y^2)\right)= \frac{xdx-ydy}{x^2+y^2}$$