Error Propagation: Why using derivatives instead of the function

Question

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 $\Delta V = \left(l+\Delta l\right)^3-l^3$