SUMS
Theorem 3. The derivative of the sum of two
or more differentiable functions of x is equal to the sum of their
derivatives. If two functions of x are given, such that
u = g(x)
and
v = h(x)
and also
then
PROOF. 
and
Subtract equation (5.1) from equation (5.2):
Rearrange this equation such that
Divide both sides of the equation by Ax and then take the
limit as
:
But, by definition
and
Then by substitution,
EXAMPLE. Find the derivative of the function
SOLUTION: Theorem 3 indicates that we should find the
derivative of each term and then show them as a sum; that is, if
and
then
PRACTICE PROBLEMS:
Find the derivative of the following:
^{}
ANSWERS:
