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By visualizing the functions $f$ and $g$ as vertical heights stacked on top of each other, a common input increment $dx$ produces separate changes $\Delta f$ and $\Delta g$. The total change in the sum $f+g$ is exactly the sum of these individual changes.

Conditions: Functions $f$ and $g$ are differentiable.; The input increment is common to both functions.

By visualizing the functions $f$ and $g$ as vertical heights stacked on top of each other, a common input increment $dx$ produces separate changes $\Delta f$ and $\Delta g$. The total change in the sum $f+g$ is exactly the sum of these individual changes.

Conditions: Functions $f$ and $g$ are differentiable.; The input increment is common to both functions.