Product Rule for Derivatives/General Result/3 Factors

Theorem
Let $\map u x$, $\map v x$ and $\map w x$ be real functions differentiable on the open interval $I$.

Then:
 * $\forall x \in I: \map {\dfrac \d {\d x} } {u v w} = u v \dfrac {\d w} {\d x} + u w \dfrac {\d v} {\d x} + v w \dfrac {\d u} {\d x}$

Proof
Let $y = u v w$.

Then: