Manipulation of Exterior Derivative

Theorem
For the exterior derivative, the following statements are true:


 * $\mathrm d \left({a b}\right) = a \mathrm d b + \left({\mathrm d a}\right) b$


 * $\mathrm d \left({a \wedge b}\right) = \mathrm d a \wedge b - a \wedge \mathrm d b$

where $a \wedge b$ is the wedge product.