Editing Binomial theorem (section)

=== General Leibniz rule ===
{{Main|General Leibniz rule}}

The general Leibniz rule gives the {{mvar|n}}th derivative of a product of two functions in a form similar to that of the binomial theorem:<ref>{{cite book |last=Olver |first=Peter J. |author-link=Peter J. Olver |year=2000 |title=Applications of Lie Groups to Differential Equations |publisher=Springer |pages=318–319 |isbn=9780387950006 |url=https://books.google.com/books?id=sI2bAxgLMXYC&pg=PA318 }}</ref> 
<math display="block">(fg)^{(n)}(x) = \sum_{k=0}^n \binom{n}{k} f^{(n-k)}(x) g^{(k)}(x).</math>

Here, the superscript {{math|(''n'')}} indicates the {{mvar|n}}th derivative of a function, <math>f^{(n)}(x) = \tfrac{d^n}{dx^n}f(x)</math>.  If one sets {{math|1=''f''(''x'') = ''e''{{sup|''ax''}}}} and {{math|1=''g''(''x'') = ''e''{{sup|''bx''}}}}, cancelling the common factor of {{math|''e''{{sup|(''a'' + ''b'')''x''}}}} from each term gives the ordinary binomial theorem.<ref>{{cite book |last1=Spivey |first1=Michael Z. |title=The Art of Proving Binomial Identities |date=2019 |publisher=CRC Press |isbn=978-1351215800 |page=71}}</ref>