AP Calc BC Worksheet
Name___________________________________
Differentation Rules
Differentiate each function with respect to the given variable.
5
5 −5
−1
1) s = − x 3 − 4x + x
3
3
3
1
5 4 5 4
−4
2) g = r − r + r
3
3
2
For each problem, find the indicated derivative with respect to x.
5
2
3) y = 4x + 3x − x
d 3y
Find 3
dx
5
3
4) y = −5x − 5x + x
d 4y
Find 4
dx
Differentiate each function with respect to x.
(
5
4
)(
5) y = x − 2 2x
2x 4 − 1
7) y = 4
5x + 3
5
− 1)
6) y = (1 + 2x
)(−2x 3 − 5)
−2
3x 4 + 2x 3
8) y =
4x 5 + 3
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9) y = ((5x 4 + 2) − 2)
4
11) y = sin (cos x 2 )
2
10) y = ((4x 4 + 5) + 2)
3
4
12) y = tan (tan 4x 2 )
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Worksheet by Kuta Software LLC
AP Calc BC Worksheet
Name___________________________________
Differentation Rules
Differentiate each function with respect to the given variable.
3
5
5 −5
−1
1) s = − x 3 − 4x + x
3
3
1
5 4 5 4
−4
2) g = r − r + r
3
3
2
ds
4
25
= −5x 2 + 2 − 6
dx
x
3x
dg
5
5
4 3
= 1 − 3 − 5
dr
r
4
4
4r
8r
For each problem, find the indicated derivative with respect to x.
5
2
3) y = 4x + 3x − x
d 3y
Find 3
dx
5
3
4) y = −5x − 5x + x
d 3y
= 4240x 2
3
dx
d 4y
Find 4
dx
d 4y
= −600x
dx 4
Differentiate each function with respect to x.
(
)(
5
4
5) y = x − 2 2x
(
5
6) y = (1 + 2x
− 1)
)
5
4
dy
5
= x − 2 ⋅ 10x 4 + (2x 5 − 1) ⋅ x
dx
4
=
25x
2
21
4
− 20x 4 −
5x
4
dy
−2
−3
= (1 + 2x ) ⋅ −6x 2 + (−2x 3 − 5) ⋅ −4x
dx
20
= −6x 2 − 4 + 3
x
1
4
1
4
2x 4 − 1
7) y = 4
5x + 3
)(−2x 3 − 5)
−2
3x 4 + 2x 3
8) y =
4x 5 + 3
dy (5x 4 + 3) ⋅ 8x 3 − (2x 4 − 1) ⋅ 20x 3
=
dx
(5x 4 + 3) 2
44x 3
=
(5x 4 + 3) 2
dy (4x 5 + 3)(12x 3 + 6x 2 ) − (3x 4 + 2x 3 ) ⋅ 20x 4
=
dx
(4x 5 + 3) 2
−12x 8 − 16x 7 + 36x 3 + 18x 2
=
(4x 5 + 3) 2
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Worksheet by Kuta Software LLC
9) y = ((5x 4 + 2) − 2)
4
2
10) y = ((4x 4 + 5) + 2)
3
dy
4
3
= 2((5x 4 + 2) − 2) ⋅ 4(5x 4 + 2) ⋅ 20x 3
dx
3
4
= 160x 3 (5x 4 + 2) ((5x 4 + 2) − 2)
11) y = sin (cos x 2 )
4
3
dy
3
2
= 4((4x 4 + 5) + 2) ⋅ 3(4x 4 + 5) ⋅ 16x 3
dx
= 192x 3 ((4x 4 + 5) + 2) ⋅ (4x 4 + 5)
3
3
2
12) y = tan (tan 4x 2 )
dy
= cos (cos x 2 ) ⋅ −sin x 2 ⋅ 2x
dx
= −2xcos (cos x 2 )sin x 2
dy
= sec 2 (tan 4x 2 ) ⋅ sec 2 4x 2 ⋅ 8x
dx
= 8xsec 2 (tan 4x 2 )sec 2 4x 2
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Worksheet by Kuta Software LLC