©D M2L0T1g3Y bKbu6tear hSBo0futTwjaZrTeA 9LwLtCq.l s VARlilZ OrciVgyh5tXst prgeksiePrnvXeXdO.2 L EMVaodNeG lwxictDhI AIcnafoi0nliqtxec oCtaSlbcOuRlTuvsg.J Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____
Date________________
Differentiation - Power, Constant, and Sum Rules
Differentiate each function with respect to
x.
1) y = 5 2) f
(
x)
= 5x183) y = 4x5 + x 4) f
(
x)
=
4x4 − 5x − 3
5) y = 3
x
5
4 6) y =
5 4
x
2 3
7) y = −4
x−5
8) y = 3 x3
9) y =
x
2
3 10) f
(
x)
= −2 4 x
-1-
©q b2b081L3S cKNuitpax uSWoffitiwHaPrYez 4LLLNCY.l 4 QAnl0lK BrOipgohutwsX FrDeDsCerrXvteBdb.x e tMdaZdSeI CwgiZtlhw NImntfdiMnoiQtweA CCeaJlkcEuClVuEse.o Worksheet by Kuta Software LLC
11) y =
2
3x4 + 5x −
x−3
12) y =
−1 2x4 + 3
x
5
3 + 2x
Differentiate each function with respect to the given variable.
13) y = −3r5 − 5r2
14) f
(
s)
=
− 3 s2
− 4 s4
15) f
(
x)
=
2 3
x
3
2 −
3 4
x
3
5 16) h
(
s)
=
2 ⋅ 3 s + 2 ⋅ 5s
Differentiate each function with respect to
x. Problems may contain constants a, b, and c.
17) y = 5c 18) y =
4a
x3a − b
x3c
-2-
©l b2M0i1x3o rKkuRtbap TSzoBfxtrwGaxrXeP YLyLhCA.c o 8A4l9lm trOiSgoh9tOsC mrpe3sfemrqvweKds.8 f cMVamdWeY EwZietshO aILnRfBiunDi9tGel yCea9lycLuLluuysN.0 Worksheet by Kuta Software LLC
Kuta Software - Infinite Calculus Name___________________________________
Period____
Date________________
Differentiation - Power, Constant, and Sum Rules
Differentiate each function with respect to
x.
1) y = 5 dy dx
= 0
2) f
(
x)
= 5x18 f'(
x)
= 90x173) y = 4x5 + x dy
dx
= 20x4 + 1
4) f
(
x)
=
4x4 − 5x − 3 f'
(
x)
= 16x3 − 55) y = 3
x
5 4
dy dx
=
15
x
1 4
4
6) y =
5 4
x
2 3
dy dx
=
5 6
x
−1 3
= 5
6
x
1 3
7) y = −4
x−5
dy dx
= 20
x−6 = 20
x6
8) y = 3 x3
dy dx
= −9
x−4 = − 9
x4
9) y =
x
2 3
dy dx
=
2 3
x
−1 3
= 2
3
x
1 3
10) f
(
x)
= −2 4 xf'
(
x)
=
−1 2
x
−3 4
= − 1
2
x
3 4
-1-
©z u2y0s1r3L QKQudtKaJ 6SwoHf0tdwUa8rmec ZLGLJC8.d c zAzlFlF Nrdilg0hJtmst ar9eMsfeHrkvpehd0.8 l wMmaidPea jwqiXt6he VIAnUfoiBnfimtbeZ 2Ciaol2couUl2uAsm.h Worksheet by Kuta Software LLC
11) y =
2
3x4 + 5x −
x−3
dy dx
=
8
3x3 + 5 + 3
x−4 =
8x3 3
+ 5 + 3
x4
12) y =
−1 2x4 + 3
x
5
3 + 2x
dy dx
=
−2x3 + 5
x
2
3 + 2
Differentiate each function with respect to the given variable.
13) y = −3r5 − 5r2 dy
dr
= −15r4 − 10r
14) f
(
s)
=
− 3 s2
− 4 s4 f'
(
s)
=
6
s−3 + 16
s−5 =
6
s3 + 16
s5
15) f
(
x)
=
2 3
x
3
2 −
3 4
x
3 5
f'
(
x)
=
x
1 2 −
9 20
x
−2 5
=
x
1
2 − 9
20
x
2 5
16) h
(
s)
=
2 ⋅ 3 s + 2 ⋅ 5s
h'
(
s)
=
1 3
s
−2
3 2 +
1 5
s
−4
5 2
=
2
3
s
2 3
+ 2
5
s
4 5
Differentiate each function with respect to
x. Problems may contain constants a, b, and c.
17) y = 5c dy dx
= 0
18) y =
4a
x3a − b
x3c
dy dx
=
12a2
x3a − 1 − 3bc
x3c − 1
-2-
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