Leibniz rule (generalized product rule)

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In calculus, the Leibniz rule, named after Gottfried Leibniz, generalizes the product rule. It states that if f and g are n-times differentiable functions, then the nth derivative of the product fg is given by

(f.g)^{(n)}=\sum_{k=0}^n {n \choose k} f^{(k)} g^{(n-k)}

where {n \choose k} is the usual binomial coefficient.

This can be proved by using the product rule and mathematical induction.

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