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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Differentiation - Logs and Exponentials
Differentiate each function with respect to
x.
1)
y =
4
4
x
4
2)
y =
4
−5
x
3
3)
y = log
3
3
x
2
4)
y = log
2
4
x
2
5)
y = log
3
(
3
x
5
+ 5
)
5
6)
y = log
5
(
−5
x
3
− 2
)
3
7)
y =
(
4
x
3
+ 2
)
3
8)
y =
3
(
x
4
+ 1
)
3
9)
y =
3
cos
3
x
4
10)
y = log
5
tan
4
x
4
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____Date________________
Differentiation - Logs and Exponentials
Differentiate each function with respect to
x.
1)
y =
4
4
x
4
dy
dx
=
4
4
x
4
ln 4 ⋅ 16
x
3
=
x
3
⋅
4
4
x
4
+ 2
ln 4
2)
y =
4
−5
x
3
dy
dx
=
4
−5
x
3
ln 4 ⋅ −15
x
2
=
−
15
x
2
ln 4
4
5
x
3
3)
y = log
3
3
x
2
dy
dx
=
1
3
x
2
ln 3
⋅ 6
x
=
2
x ln 3
4)
y = log
2
4
x
2
dy
dx
=
1
4
x
2
ln 2
⋅ 8
x
=
2
x ln 2
5)
y = log
3
(
3
x
5
+ 5
)
5
dy
dx
=
1
(
3
x
5
+ 5
)
5
ln 3
⋅ 5
(
3
x
5
+ 5
)
4
⋅ 15
x
4
=
75
x
4
ln 3 ⋅
(
3
x
5
+ 5
)
6)
y = log
5
(
−5
x
3
− 2
)
3
dy
dx
=
1
(
−5
x
3
− 2
)
3
ln 5
⋅ 3
(
−5
x
3
− 2
)
2
⋅ −15
x
2
=
−
45
x
2
ln 5 ⋅
(
−5
x
3
− 2
)
7)
y =
(
4
x
3
+ 2
)
3
dy
dx
=
3
(
4
x
3
+ 2
)
2
⋅
4
x
3
ln 4 ⋅ 3
x
2
=
9
x
2
(
4
x
3
+ 2
)
2
⋅
4
x
3
ln 4
8)
y =
3
(
x
4
+ 1
)
3
dy
dx
=
3
(
x
4
+ 1
)
3
ln 3 ⋅ 3
(
x
4
+ 1
)
2
⋅ 4
x
3
=
4
x
3
⋅
3
(
x
4
+ 1
)
3
+ 1
⋅
(
x
4
+ 1
)
2
ln 3
9)
y =
3
cos
3
x
4
dy
dx
=
3
cos
3
x
4
ln 3 ⋅ −1sin
3
x
4
⋅ 12
x
3
=
−4
x
3
⋅
3
cos
3
x
4
+ 1
sin
3
x
4
⋅ ln 3
10)
y = log
5
tan
4
x
4
dy
dx
=
1
tan
4
x
4
⋅ ln 5
⋅
sec
2
4
x
4
⋅ 16
x
3
=
16
x
3
⋅
sec
2
4
x
4
tan
4
x
4
⋅ ln 5
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