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Monday, February 17
The week’s objectives:
Monday – Lecture 3.7
Tuesday – Lecture 3.8
Wed – no class day to work
3.7 webassign due Wed
.
Thursday – Review Day
3.8 webassign due Thurs.
Friday – Test #2  covers up through section 3.8
3.7
I. Derivatives of Logarithmic Functions
II. Method of differentiation
“logarithmic differentiation”
I.
Use def’n of logs and implicit differentiation to derive the derivative
formula for
y
= log
a
(
x
)
dy/dx =
Also, note the special case if the base of the logarithm is e
Then
y = lnx
and
dy/dx =
Examples:
Find the derivative of the given functions
a)
s
(
t
) = ln(4
t
3
+ 3
t
+
b
2
)
s
(
t
) =
b)
F
(
y
) =
y
ln(1+
e
y
)
note:
the indep. var. is y (not what you’re used
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View Full Document to seeing ; this problem is #12 on p.245)
o
F
(
y
) =
c)
y
= ln(
x
4
sin
2
x
)
note: #14 in our text p.245
dy
dx
=
d)
y
= log
3
(2  7
x
)
dy
dx
=
II.
The calculation of derivatives of complicated functions involving
products, quotients, or powers can often be simplified by taking
logarithms.
The method is called “logarithmic differentiation”.
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This note was uploaded on 04/12/2008 for the course MA 141 taught by Professor Wears during the Spring '07 term at N.C. State.
 Spring '07
 WEARS
 Derivative

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