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Proposition: Generalized Product Rule
Let $f,g:D\to\mathbb R$ be $n$ times differentiable. The $n$-th derivative of the product $fg$ is given by
$$\frac{d^kf(x)g(x)}{dx^k}=\sum_{k=0}^n\binom nkf^{(n-k)}(x)g^{(k)}(x),$$
where $\binom nk$ denotes the binomial coefficient.
Table of Contents
Proofs: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
