is there any proof for the Leibniz rule for successive differentiation
$(uv)^{(n)}=\sum\limits_{k=0}^n\binom{k}{n}u^{(n-k)}v^{(k)}$
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Yes, of course there is. I think induction, making use of the ordinary Leibniz rule, and Pascal's identity should do it. – Matthew Leingang Feb 07 '18 at 09:17
