Product Rule
Although the partial derivative exhibits a product rule, the geometric derivative only partially inherits this property. Consider two functions F and G:
Since the geometric product is not commutative with in general, we cannot proceed further without new notation. A solution is to adopt the overdot notation, in which the scope of a geometric derivative with an overdot is the multivector-valued function sharing the same overdot. In this case, if we define
then the product rule for the geometric derivative is
Read more about this topic: Geometric Calculus, Differentiation
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