 UBC Calculus Online Course Notes 
Differentiating Products of FunctionsMany functions are built by multiplying two simpler functions. For example, is the product of the linear function and the function On this page, we will verify the
As always, we'll compute the average rate of change of the function over the interval to This average rate of change is Our argument will use the tangent line approximation to compute the approximate average rate of change. Remember that
and that these approximations are very good when
is
small.
If we multiply these two approximations together, we see that
