Properties of Differentiation
Let be an [[N-form|form]] and , an form, and a form. Then, the following identities
d(d\omega)&=&0\\ d(\omega+\mu)&=&d\omega+d\mu\\ d(\omega\wedge\mu)&=&d\omega\wedge\nu+(-1)^n\omega\wedge d\mu\\ d(f\wedge dx_1\wedge\cdots\wedge dx_n)&=&df\wedge dx_1\wedge\cdots\wedge dx_n\\ df&=&\dfrac{\partial f}{\partial x_1}dx_1+\cdots+\dfrac{\partial f}{\partial x_x}dx_x \end{eqnarray}$$ ## References [[Bachman, D. - A geometric approach to differential forms|@Bac12]]