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Review of DiFerentiation and AntidiFerentiation
As we begin Calculus II it is assumed that the student has covered the derivative of a function in
some detail and has learned how to Fnd the antiderivative of basic functions. This section is provided
as a summary of some of these topics. Knowledge of trigonometric functions, exponential functions, and
logarithmic functions is assumed, but will be reviewed as necessary throughout the course for reinforcement.
Defnition oF derivative
.
Suppose
f
is deFned on an open interval containing
x
. The derivative of
f
at
x
is deFned by
D
x
(
f
(
x
)) =
f
0
(
x
)
≡
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
Tangent line
.I
f
f
(
x
0
)=
y
0
and
f
0
(
x
0
m
, then an equation for the line tangent to the curve
y
=
f
(
x
)
is given by
y
−
y
0
=
m
(
x
−
x
0
)
Rules of DiFerentiation
Assume that
a
and
b
are real numbers and that
f
(
x
) and
g
(
x
) are di±erentiable
on an open interval containing
x
.
Rule 1. The derivative is linear. That is,
D
x
(
af
(
x
)+
bg
(
x
)
)
=
aD
x
(
f
(
x
)) +
bD
x
(
g
(
x
)) =
af
0
(
x
bg
0
(
x
).
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 Spring '08
 Iacob
 Derivative

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