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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Differentiation - Natural Logs and Exponentials
Differentiate each function with respect to
x.
1)
y = ln
x
3
2)
y =
e
2
x
3
3)
y = ln ln 2
x
4
4)
y = ln ln 3
x
3
5)
y = cos
ln 4
x
3
6)
y =
e
e
3
x
2
7)
y =
e
(
4
x
3
+ 5
)
2
8)
y =
ln 4
x
2
⋅
(
−
x
3
− 4
)
9)
y = ln
(
−
4
x
4
x
3
− 3
)
5
10)
y =
e
5
x
4
e
4
x
2
+ 3
©
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Differentiation - Natural Logs and Exponentials
Differentiate each function with respect to
x.
1)
y = ln
x
3
dy
dx
=
1
x
3
⋅ 3
x
2
=
3
x
2)
y =
e
2
x
3
dy
dx
=
e
2
x
3
⋅ 6
x
2
3)
y = ln ln 2
x
4
dy
dx
=
1
ln 2
x
4
⋅
1
2
x
4
⋅ 8
x
3
=
4
x ln 2
x
4
4)
y = ln ln 3
x
3
dy
dx
=
1
ln 3
x
3
⋅
1
3
x
3
⋅ 9
x
2
=
3
x ln 3
x
3
5)
y = cos
ln 4
x
3
dy
dx
=
−sin
ln 4
x
3
⋅
1
4
x
3
⋅ 12
x
2
=
−
3sin
ln 4
x
3
x
6)
y =
e
e
3
x
2
dy
dx
=
e
e
3
x
2
e
3
x
2
⋅ 6
x
=
6
x
e
e
3
x
2
+ 3
x
2
7)
y =
e
(
4
x
3
+ 5
)
2
dy
dx
=
e
(
4
x
3
+ 5
)
2
⋅ 2
(
4
x
3
+ 5
)
⋅ 12
x
2
=
24
x
2
e
(
4
x
3
+ 5
)
2
(
4
x
3
+ 5
)
8)
y =
ln 4
x
2
⋅
(
−
x
3
− 4
)
dy
dx
=
ln 4
x
2
⋅ −3
x
2
+
(
−
x
3
− 4
)
⋅
1
4
x
2
⋅ 8
x
=
−3
x
3
ln 4
x
2
− 2
x
3
− 8
x
9)
y = ln
(
−
4
x
4
x
3
− 3
)
5
dy
dx
=
5
(
1
−4
x
4
⋅ −16
x
3
−
1
x
3
− 3
⋅ 3
x
2
)
=
5
(
x
3
− 12
)
x
(
x
3
− 3
)
(Rules of logarithms used)
10)
y =
e
5
x
4
e
4
x
2
+ 3
dy
dx
=
e
5
x
4
−
(
4
x
2
+ 3
)
(
20
x
3
−
8
x
)
=
4
x
e
5
x
4
− 4
x
2
− 3
(
5
x
2
− 2
)
(Rules of exponents used)
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