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MATH1010U:
Chapter 3
1
DIFFERENTIATION RULES
Derivatives of Polynomials and Exponential Functions(3.1,p173)
Recall:
Last day, we learned how to find the derivative from first principles.
Now, let’s consider some useful rules to help us do differentiation.
Derivative of a Constant Function:
0
)
(
=
c
dx
d
The Power Rule
(General Version):
If
n
is any real number, then
1
)
(
−
=
n
n
x
n
x
dx
d
The Constant Multiple Rule:
If
c
is a constant and
f
is a differentiable function, then
)
(
))
(
(
x
f
dx
d
c
x
f
c
dx
d
⋅
=
⋅
The Sum Rule:
If
f
and
g
are both differentiable, then
[]
)
(
)
(
)
(
)
(
x
g
dx
d
x
f
dx
d
x
g
x
f
dx
d
+
=
+
The Difference Rule:
If
f
and
g
are both differentiable, then
[]
)
(
)
(
)
(
)
(
x
g
dx
d
x
f
dx
d
x
g
x
f
dx
d
−
=
−
Now that we know how to differentiate polynomials, let’s consider some other functions,
e.g. the exponential function.
Exponential Function
Recall:
Earlier in the course, we introduced the exponential function.

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MATH1010U:
Chapter 3
2
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