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MAT 1330, Fall 2010 Assignment 4
Due Wednesday November 10, at the beginning of class.
Late assignments will not be accepted; nor will unstapled assignments.
Instructor (circle one): Frithjof Lutscher
Angelika Welte
Aziz Khanchi
Robert Smith?
DGD (circle one): 1
2
3
4
Student Name
Student Number
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Question 1.
Find the derivatives of the following functions. Do not simplify.
a)
f
(
x
) = cos(
x
) sin(5
x
2
+ 7),
f
!
(
x
)=
−
sin(
x
) sin(5
x
2
+7)+cos(
x
)[cos(5
x
2
+ 7)10
x
]
,
Use the quotient rule and
the chain rule.
b)
g
(
x
tan(
x
)
e
7
x
x
4
,
g
!
(
x
e
7
x
x
4
cos
2
x
−
tan(
x
)[7
e
7
x
x
4
+
e
7
x
4
x
3
]
(
e
7
x
x
4
)
2
Use the quotient rule and the
product rule.
c)
h
(
x
e
cos
3
x
+2 sin
2
x
,
h
!
(
x
e
cos
3
x
+2 sin
2
x
[3 cos
2
(
x
)(
−
sin(
x
)) + 4 sin(
x
) cos(
x
)]
Use the chain rule twice.
d)
w
(
y
) = ln(
!
y
2
+3
y
+ 9),
w
!
(
y
1
!
y
2
y
+9
1
2
·
!
y
2
y
(2
y
+3)
Use the chain rule twice or use properties of log and then the chain rule.
e)
u
(
z
sin(
z
5
)
√
z
,
u
!
(
z
cos(
z
5
)(5
z
4
)
√
z
−
sin(
z
5
)
1
2
√
z
z
Use the quotient rule and the chain rule.
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 Fall '08
 DUMITRISCU

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