Kuta Software - Infinite Calculus
Name___________________________________
Differentiation - Quotient Rule
Date________________ Period____
Differentiate each function with respect to x.
1) y =
2
2x4 − 5
3) f ( x) =
5
3
4x + 4
3x4 + 2
5) y = 3
3x − 2
7) y =
4x5 + x2 + 4
5x2 − 2
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2) f ( x) =
4) y =
2
x5 − 5
4x3 − 3x2
4x5 − 4
4x5 + 2x2
6) y =
3x4 + 5
8) y =
-1-
3x4 + 5x3 − 5
2x4 − 4
Worksheet by Kuta Software LLC
x3 − x2 − 3
9) y =
x5 + 3
10) y =
x4 + 6
3 − 4x
11) y =
−4
4x4 − 4x2 + 5
5
3
2x + 3
Critical thinking question:
12) A classmate claims that
()
f ' f'
=
for any functions f and g. Show an example that proves your
g
g'
classmate wrong.
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus
Name___________________________________
Differentiation - Quotient Rule
Date________________ Period____
Differentiate each function with respect to x.
1) y =
2
2x4 − 5
2) f ( x) =
2 ⋅ 8x3
dy
=−
dx
(2 x 4 − 5) 2
16 x 3
=− 8
4 x − 20 x 4 + 25
3) f ( x) =
5
3
4x + 4
f ' ( x) = −
f ' ( x) = −
=−
4) y =
(4 x 3 + 4) 2
15 x 2
=− 6
4x + 8x3 + 4
4x5 + x2 + 4
5x2 − 2
x 10
10 x 4
− 10 x 5 + 25
4x3 − 3x2
4x5 − 4
dy (3 x 4 + 5)(20 x 4 + 4 x) − (4 x 5 + 2 x 2 ) ⋅ 12 x 3
=
dx
(3 x 4 + 5) 2
12 x 8 − 12 x 5 + 100 x 4 + 20 x
=
9 x 8 + 30 x 4 + 25
8) y =
dy (5 x 2 − 2)(20 x 4 + 2 x) − (4 x 5 + x 2 + 4) ⋅ 10 x
=
dx
(5 x 2 − 2) 2
60 x 6 − 40 x 4 − 44 x
=
25 x 4 − 20 x 2 + 4
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( x 5 − 5) 2
4x5 + 2x2
6) y =
3x4 + 5
dy (3 x 3 − 2) ⋅ 12 x 3 − (3 x 4 + 2) ⋅ 9 x 2
=
dx
(3 x 3 − 2) 2
9 x 6 − 24 x 3 − 18 x 2
=
9 x 6 − 12 x 3 + 4
7) y =
2 ⋅ 5x4
dy (4 x 5 − 4)(12 x 2 − 6 x) − (4 x 3 − 3 x 2 ) ⋅ 20 x 4
=
dx
(4 x 5 − 4) 2
−8 x 7 + 9 x 6 − 12 x 2 + 6 x
=
4 x 10 − 8 x 5 + 4
5 ⋅ 12 x 2
3x4 + 2
5) y = 3
3x − 2
2
x5 − 5
3x4 + 5x3 − 5
2x4 − 4
dy (2 x 4 − 4)(12 x 3 + 15 x 2 ) − (3 x 4 + 5 x 3 − 5) ⋅ 8 x 3
=
dx
(2 x 4 − 4) 2
−5 x 6 − 4 x 3 − 30 x 2
=
2x8 − 8x4 + 8
-1-
Worksheet by Kuta Software LLC
x3 − x2 − 3
9) y =
x5 + 3
dy ( x 5 + 3)(3 x 2 − 2 x) − ( x 3 − x 2 − 3) ⋅ 5 x 4
=
dx
( x 5 + 3) 2
−2 x 7 + 3 x 6 + 15 x 4 + 9 x 2 − 6 x
=
x 10 + 6 x 5 + 9
10) y =
x4 + 6
3 − 4x
−4
−4
−5
dy (3 − 4 x ) ⋅ 4 x 3 − ( x 4 + 6) ⋅ 16 x
=
dx
(3 − 4 x −4 ) 2
12 x 11 − 32 x 7 − 96 x 3
=
9 x 8 − 24 x 4 + 16
11) y =
4x4 − 4x2 + 5
5
3
2x + 3
dy
=
dx
=
(
5
3
)
2
10 3
2 x + 3 (16 x − 8 x) − (4 x − 4 x + 5) ⋅
x
3
3
4
(2x + 3)
5
3
56 x
14
3
2
2
8
3
3
+ 144 x − 8 x − 72 x − 50 x
12 x
10
3
2
3
5
3
+ 36 x + 27
Critical thinking question:
12) A classmate claims that
()
f ' f'
=
for any functions f and g. Show an example that proves your
g
g'
classmate wrong.
Many answers. Ex: f = 4, g = 2 x, −
2
≠0
x2
Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC