M1314 Lesson 4 1
Math 1314
Lesson 4
Basic Rules of Differentiation
We can use the limit definition of the derivative to find the derivative of every function,
but it isn’t always convenient. Fortunately, there are some rules for finding derivatives
which will make this easier.
First, a bit of notation:
[ ]
)(xf
dx
d is a notation that means “the derivative of
f
with respect to
x
, evaluated at
x
.”
Rule 1: The Derivative of a Constant
[ ]
,0=
c
dx
d
where
c
is a constant.
Example 1
: If
,17)(
−
=
xf find )(' xf .
Rule 2: The Power Rule
[
]
1−
=
nn
nxx
dx
d for any real number n
Example 2
: If ,)(
5
xxf
=
find )(' xf .
Example 3
: If xxf =)( , find )(' xf .
