# Intuition of product rule using graphs and slopes

I have seen formal proof of the product rule ($$(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)$$) and one with rectangles and areas - explanation seems reasonable. But, is there direct and intuitive proof using only graphs ($$\mathbb{R}^2$$ plane), slopes and "ordinary" functions, inputs and outputs? Thanks!