General Leibniz rule

In calculus, the general Leibniz rule,[1] named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if and are -times differentiable functions, then the product is also -times differentiable and its th derivative is given by

where is the binomial coefficient and denotes the jth derivative of f (and in particular ).

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

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