r = 0.5 #radius cm = 1/2 diameter
dr = 0.1 #accuracy 1mm = 0.1cm
V = expression(4/3*pi*r^3) # volume of a sphere
vr = D(V, "r") # first derivative: v'(r)
dV = round(eval(vr) * dr, 5) # propagated error: dV = vr * +/- dr
print(paste("+/-",dV))## [1] "+/- 0.31416"