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Kuta Software - Infinite Calculus
Name___________________________________
Differentiation - Chain Rule
Date________________ Period____
Differentiate each function with respect to x
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x
-1-
3
−2 x 2 + 1
−2
Worksheet by Kuta Software LLC
9) y = (3 x 3 + 1)(−4 x 2 − 3) 4
10) y =
( x 3 + 4) 5
3x4 − 2
11) y = (( x + 5) − 1)
5
12) y = (5 x 3 − 3) 5
4
4
−4 x 5 − 3
Critical thinking question:
13) Give a function that requires three applications of the chain rule to differentiate
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...
5
1) y = ( x 3 + 3)
dy
4
= 5( x 3 + 3) ⋅ 3 x 2
dx
4
= 15 x 2 ( x 3 + 3)
3) y = (−5 x 3 − 3)
2) y = (−3 x 5 + 1)
dy
2
= 3(−3 x 5 + 1) ⋅ −15 x 4
dx
2
= −45 x 4 (−3 x 5 + 1)
3
4) y = (5 x 2 + 3)
dy
= 3(−5 x 3 − 3) 2 ⋅ −15 x 2
dx
2
= −45 x 2 (−5 x 3 − 3)
5) f ( x) =
4
3
7) f ( x) =
3
− 2)
−
1
f ' ( x) = (−2 x 2 + 1) 2 ⋅ −4 x
2
2x
=−
3
4
(−2 x
−2 x 4 + 5
8) y = (− x 4 − 3)
2
3(−2 x + 5)
2
3
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...
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...
Then differentiate the
function
...
Free trial available at KutaSoftware
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...
0
-2-
Worksheet by Kuta Software LLC