Question

(challenge) Proving the Product Rule for differentiation and integration:
Is there a way to visually demonstrate this as a proof? There are several written examples, but this would be how to explain it to a visual or spatial learner instead.

For reference:
\[\frac{d}{dx}U*V=U \frac{d}{dx}V+V \frac{d}{dx}U\]
\[\int\limits U\cdot dV = U\cdot V-\int\limits V\cdot dU\]