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Kuta Software - Infinite Calculus Name___________________________________ 
Differentiation - Chain Rule Date________________ Period____ 
Differentiate each function with respect to 
x. 
1) 
y = 
( 
x3 + 3)5 
2) 
y = 
( 
−3 
x5 + 1)3 
3) 
y = 
( 
−5 
x3 − 3)3 
4) 
y = 
5 
x2 + 3)4 
( 
5) 
f ( 
x) = 
4 
−3 
x4 − 2 6) 
f ( 
x) = 
−2 
x2 + 1 
7) 
f ( 
x) = 
3 
−2 
x4 + 5 8) 
y = 
− 
x4 − 3)−2 
( 
-1- 
©Z A280m1W3z EKjuhtmaZ NSloMf1tEwjaXrXem rL6LwCT.G R QAXldlL prFiVgAhItCsH UrreksaehruvueOdH.f w sMeaUdie8 Ew3iVtkhf aIrntfpiGngi1tEe5 2CJaGlQcTuelKuhsh.x Worksheet by Kuta Software LLC
9) 
y = 
( 
3 
x3 + 1) 
( 
−4 
x2 − 3)4 
10) 
y = 
x3 + 4)5 
3 
x4 − 2 
( 
11) 
y = 
( 
( 
x + 5)5 
− 1)4 
12) 
y = 
5 
x3 − 3)5 4 
( 
−4 
x5 − 3 
Critical thinking question: 
13) Give a function that requires three applications of the chain rule to differentiate. Then differentiate the 
function. 
-2- 
©F f2h021D34 0KmuFtHaQ DSBocfDtEwXaErXe2 BLRLYC7.c r TAklrl4 Irxiog3hDt1sc lrmeAsOesrJvsewda.V R MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve6 XCtajlQc3uwlfuxs8.6 Worksheet by Kuta Software LLC

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Derivative worksheet1

  • 1. Kuta Software - Infinite Calculus Name___________________________________ Differentiation - Chain Rule Date________________ Period____ Differentiate each function with respect to x. 1) y = ( x3 + 3)5 2) y = ( −3 x5 + 1)3 3) y = ( −5 x3 − 3)3 4) y = 5 x2 + 3)4 ( 5) f ( x) = 4 −3 x4 − 2 6) f ( x) = −2 x2 + 1 7) f ( x) = 3 −2 x4 + 5 8) y = − x4 − 3)−2 ( -1- ©Z A280m1W3z EKjuhtmaZ NSloMf1tEwjaXrXem rL6LwCT.G R QAXldlL prFiVgAhItCsH UrreksaehruvueOdH.f w sMeaUdie8 Ew3iVtkhf aIrntfpiGngi1tEe5 2CJaGlQcTuelKuhsh.x Worksheet by Kuta Software LLC
  • 2. 9) y = ( 3 x3 + 1) ( −4 x2 − 3)4 10) y = x3 + 4)5 3 x4 − 2 ( 11) y = ( ( x + 5)5 − 1)4 12) y = 5 x3 − 3)5 4 ( −4 x5 − 3 Critical thinking question: 13) Give a function that requires three applications of the chain rule to differentiate. Then differentiate the function. -2- ©F f2h021D34 0KmuFtHaQ DSBocfDtEwXaErXe2 BLRLYC7.c r TAklrl4 Irxiog3hDt1sc lrmeAsOesrJvsewda.V R MMtaOdJeL KwQiIt2hG DINnYfGiUn0igtve6 XCtajlQc3uwlfuxs8.6 Worksheet by Kuta Software LLC