Manipulation of Exterior Derivative

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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.


Proof