In Almering e.a. (6de druk) lezen we:
$
\eqalign{
& \left[ {f(a) \cdot g(a)} \right]^' = \cr
& \mathop {\lim }\limits_{x \to a} \frac{{\left( {f \cdot g} \right)\left( x \right) - \left( {f \cdot g} \right)\left( a \right)}}
{{x - a}} = \cr
& \mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right) \cdot g\left( x \right) - f\left( a \right) \cdot g\left( a \right)}}
{{x - a}} = \cr
& \mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right) \cdot g\left( x \right) - f\left( a \right) \cdot g\left( a \right) - f\left( a \right) \cdot g\left( x \right) + f\left( a \right) \cdot g\left( x \right)}}
{{x - a}} = \cr
& \mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right) \cdot g\left( x \right) - f\left( a \right) \cdot g\left( x \right) - f\left( a \right) \cdot g\left( a \right) + f\left( a \right) \cdot g\left( x \right)}}
{{x - a}} = \cr
& \mathop {\lim }\limits_{x \to a} \frac{{\left( {f\left( x \right) - f\left( a \right)} \right) \cdot g\left( x \right) + f\left( a \right) \cdot \left( {g\left( x \right) - g\left( a \right)} \right)}}
{{x - a}} = \cr
& \mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right) - f\left( a \right)}}
{{x - a}}\mathop {\lim }\limits_{x \to a} g\left( x \right) + f\left( a \right) \cdot \mathop {\lim }\limits_{x \to a} \frac{{g\left( x \right) - g\left( a \right)}}
{{x - a}} = \cr
& f'\left( a \right) \cdot g\left( a \right) + f\left( a \right) \cdot g'\left( a \right) \cr}
$
