General Leibniz rule
In calculus, the general Leibniz rule, 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
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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.