 UBC Calculus Online Course Notes 
Differentiating Sums of FunctionsMany functions are built by summing two simpler functions. For example, is the sum of the identity function and the constant function We will verify the
Differentiating sums is pretty easy. Let's consider the average rate of change of the function over the interval to
This shows that the average rate of change of the sum is just the sum of the average rates of change of and As becomes very small, the two average rates of change are very close to the derivatives and This shows us that
