Derivative/R/Product of n functions/Exercise

Let ${}D\subseteq \mathbb {R}$ be a subset and let

$f_{i}\colon D\longrightarrow \mathbb {R} ,\,i=1,\ldots ,n,$

be differentiable functions. Prove the formula

${}{\left(f_{1}\cdots f_{n}\right)}'=\sum _{i=1}^{n}f_{1}\cdots f_{i-1}f_{i}'f_{i+1}\cdots f_{n}\,.$

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