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The formula for the volume of a cube is V=s^3.

Take the first derivative----> d/dt(V)= d/dt(s^3) ---->dv/dt= 3s^2 (ds/dt)

dv/dt is the propagated error for volume, so the other variables should already be defined in the question where:

s= side length and ds/dt would equal possible error in each side.

Sometimes it's necessary to solve for these variables using other formulas the most common of which is surface area which is:

SA=6s^2 where SA`= dsa/dt= 12s (ds/dt).

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Q: How do you use differentials to estimate the propagated error in computing the volume of a cube?
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