# How can I find the derivative of a combinatorial expression? [closed]

I want to differentiate the following equation:

n = (nchoosek)*p*(1 - p)^(n - k)


After differentiating my result is:

n = -1/log(1 - p)


But my problem is that I cannot differentiate this. Can anyone please help me to do this?

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## closed as unclear what you're asking by m_goldberg, Artes, Sjoerd C. de Vries, Michael E2, The Toad♦Nov 17 '13 at 6:34

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

Is this a question about how to use Mathematica or about solving a math problem? –  Szabolcs Nov 16 '13 at 18:44
Your equation is not actually an equation, since it has no equals sign anywhere in it. Also, what are you trying to do? –  DumpsterDoofus Nov 16 '13 at 18:50
derivative with respect to what? –  Nasser Nov 16 '13 at 19:19

If you are trying to take the derivative of $\binom{n}{k}p(1-p)^{n-k}$ where "nchoosek" is $\binom{n}{k}=\frac{n!}{k!(n-k)!}$ with respect to $p$ in Mathematica, or specifically, compute $$\frac{d}{dp}\binom{n}{k}p(1-p)^{n-k},$$ then you can do this with
D[n!/(k! (n - k)!)*p*(1 - p)^(n - k), p] // Simplify

If you are trying to differentiate with respect to one of the other terms, then change the last $p$ in that code to the other term and see what happens.