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The sum rule is visualized by stacking vertical heights, where an input increment causes additive changes in height ($(f+g)'=f'+g'$). In contrast, the product rule is visualized as an expanding rectangle with sides $f(x)$ and $g(x)$, where the area change consists of two rectangular strips and a small corner square ($\Delta(fg) = g\Delta f + f\Delta g + \Delta f \Delta g$).

Conditions: Comparing linear combination vs multiplicative interaction; Using geometric models for differentiation

The sum rule is visualized by stacking vertical heights, where an input increment causes additive changes in height ($(f+g)'=f'+g'$). In contrast, the product rule is visualized as an expanding rectangle with sides $f(x)$ and $g(x)$, where the area change consists of two rectangular strips and a small corner square ($\Delta(fg) = g\Delta f + f\Delta g + \Delta f \Delta g$).

Conditions: Comparing linear combination vs multiplicative interaction; Using geometric models for differentiation