# Error Propagation: Why using derivatives instead of the function [duplicate]

Suppose I've measured the length $$l$$ with an uncertainty $$\Delta l$$ in order to calculate the Volume of a cube $$V = l^3$$. If I were to add an error: why am I supposed to do it like $$\Delta V = \sqrt{\left(\partial_l V\right)^2\,\left(\Delta l\right)^2}$$ and not just $$\Delta V = \left(l+\Delta l\right)^3-l^3$$