The relative change of $f$ is $\Delta f / f$

For example, the relative change in the volume of a square cube with edges of length $x$, when the change in the lengths of the cube is $\Delta x$

$\frac{\Delta V}{V} = \frac{3 x^2 \Delta x}{x^3} = \frac{3 \Delta x}{x}$

Consider a sphere will volume $V = \frac{4}{3} \pi r^3$

If $r$ changes by $\Delta r$, then $\Delta V \simeq$ $r^2 \Delta r$

The relative change is approximately $\frac{\Delta r}{r}$

Question

The relative change of $f$ is $\Delta f / f$

For example, the relative change in the volume of a square cube with edges of length $x$, when the change in the lengths of the cube is $\Delta x$

$\frac{\Delta V}{V} = \frac{3 x^2 \Delta x}{x^3} = \frac{3 \Delta x}{x}$

Consider a sphere will volume $V = \frac{4}{3} \pi r^3$

If $r$ changes by $\Delta r$, then $\Delta V \simeq$   $r^2 \Delta r$

The relative change is approximately   $\frac{\Delta r}{r}$