When you learned operations such as multiplication you only learned results such as 5x3=15. If you needed to compute the product of 5x3x4 you used the idea of associativity. You computed 5x3-15 and then multiplied 15x4-60. This could be denoted by (5×3) x4. 1. Since you know how to find the derivative of a product of two functions, use the idea of associativity to find the derivative of the product of three functions f.g. and h. Your answer should involve f.f'.8. g',h, and h'. (Do not use specific functions. Just use f.g. and has functions.)
When you learned operations such as multiplication you only learned results such as 5x3=15. If you needed to compute the product of 5x3x4 you used the idea of associativity. You computed 5x3-15 and then multiplied 15x4-60. This could be denoted by (5×3) x4. 1. Since you know how to find the derivative of a product of two functions, use the idea of associativity to find the derivative of the product of three functions f.g. and h. Your answer should involve f.f'.8. g',h, and h'. (Do not use specific functions. Just use f.g. and has functions.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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TT
.
xh
Using the product rule to get the chain rule
When you learned operations such as multiplication you only learned results
such as 5x3=15. If you needed to compute the product of 5x3x4 you used
the idea of associativity. You computed 5x3 =15 and then multiplied
15x4-60. This could be denoted by (5x3)×4.
1. Since you know how to find the derivative of a product of two
functions, use the idea of associativity to find the derivative of the
product of three functions f.g. and h. Your answer should involve
f.f.8. g',h, and h'. (Do not use specific functions. Just use
f.g. and has functions.)
2. Use your result from part 1 to find the derivative of the product
fxfxf or f³.
3. Find a rule for the derivative of the product of four functions
f.g.h, and k.
4. Use your result from part 3 to find the derivative of the product
fxfxfxf or fª.
5. What do you think the derivative of f" is for any positive integer n?
6. Use the rule you found in part 5 to compute the derivative of sin¹ x.
0
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