Recognizing that
we can approximate
using
We can easily compute
Without calculus, this is the best approximation we could reasonably come up with. The total differential gives us a way of adjusting this initial approximation to hopefully get a more accurate answer.
We let The total differential is approximately equal to so
Approximating with 4 gives approximating with gives Thus
We, of course, can compute the actual value of
with a calculator; the actual value, accurate to 5 places after the decimal, is
Obviously our approximation is quite good.