Quiz
1. If
f
(
x
) =
x
2
e
x
, find
f
0
(
x
).
2. If
g
(
x
) =
sin(
x
)
1 + cos(
x
)
, find
g
0
(
x
).
3. If
h
(
x
) =
x
7
+ 3
x
6
-
5
x
3
+ 2
x
2
-
x
+ 1, find
h
0
(
x
) and
h
00
(
x
).
4. Find the equation of the tangent line to the curve
y
= (1
-
2
x
)
100
at the point (0
,
1).
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Solutions
1.
f
0
(
x
) =
d
dx
(
x
2
)e
x
+
x
2
d
dx
e
x
= 2
x
e
x
+
x
2
e
x
=
x
e
x
(2 +
x
).
2. If g(x)=sin(x) / (1+cos(x)), find
g
0
(
x
) =
(1 + cos(
x
))
d
dx
(sin(
x
))
-
sin(
x
)
d
dx
(1 + cos(
x
))
(1 + cos(
x
))
2
=
(1 + cos(
x
)) cos(
x
)
-
sin(
x
)(
-
sin(
x
))
(1 + cos(
x
))
2
=
cos(
x
) + cos
2
(
x
) + sin
2
(
x
)
(1 + cos(
x
))
2
=
cos(
x
) + 1
(1 + cos(
x
))
2
=
1
1 + cos(
x
)
.
3.
h
0
(
x
) = 7
x
6
+ 18
x
5
-
15
x
2
+ 4
x
-
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- Spring '10
- zeck
- Math, Slope, Cos
-
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