Definition
Product Rule
Let
be an open interval and let be differentiable functions. Then the product is differentiable on and its derivative is: In Leibniz notation:
Intuition
Area of a rectangle
Regard
and as the side lengths of a rectangle. A small change produces changes and . The change in area is the sum of two strips, neglecting the vanishingly small corner: Dividing by
and taking the limit gives the product rule.