Q.#8 To date, we have used the standard form of the Chain Rule: [f(g(x)]' = f'(g(x)) g'(x). used by rewriting composition with: There also is an alternate form: dy dy du dx du dx u=g(x) for the inner function y=f(g(x))=f(u) for the outer function For example, h(x)=f(g(x)) = (3x+5) ³ becomes y=f(u) = u³3, where u = 3x +5 Using the above, please find the derivative of h(x) = f(g(x)) = (3x + 5)³ using: Final Answer a) Standard Form of Chain Rule: [f(g(x)] = f'(g(x)) g'(x) = b) Alternate Form of Chain Rule: dy dy du dx du dx Final Answer
Q.#8 To date, we have used the standard form of the Chain Rule: [f(g(x)]' = f'(g(x)) g'(x). used by rewriting composition with: There also is an alternate form: dy dy du dx du dx u=g(x) for the inner function y=f(g(x))=f(u) for the outer function For example, h(x)=f(g(x)) = (3x+5) ³ becomes y=f(u) = u³3, where u = 3x +5 Using the above, please find the derivative of h(x) = f(g(x)) = (3x + 5)³ using: Final Answer a) Standard Form of Chain Rule: [f(g(x)] = f'(g(x)) g'(x) = b) Alternate Form of Chain Rule: dy dy du dx du dx Final Answer
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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![Q.#8
To date, we have used the standard form of the Chain Rule: [f(g(x)] = f'(g(x)) g'(x).
There also is an alternate form:
dy du
used by rewriting composition with:
du dx
dy
dx
u=g(x) for the inner function
y=f(g(x)) =f(u) for the outer function
For example, h(x) = f(g(x)) = (3x+5) ³ becomes y=f(u) = u³, where u = 3x + 5
Using the above, please find the derivative of h(x) = f(g(x)) = (3x + 5)³ using:
Final Answer
a) Standard Form of Chain Rule:
[f(g(x)]' = f'(g(x)) g'(x)
b) Alternate Form of Chain Rule:
dy dy du
dx du dx
Final Answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbed15dc4-f7d5-4c59-88ec-c5b05b5850af%2F2d693750-93fa-495a-907f-843989aeeaae%2Fvxn7p9n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q.#8
To date, we have used the standard form of the Chain Rule: [f(g(x)] = f'(g(x)) g'(x).
There also is an alternate form:
dy du
used by rewriting composition with:
du dx
dy
dx
u=g(x) for the inner function
y=f(g(x)) =f(u) for the outer function
For example, h(x) = f(g(x)) = (3x+5) ³ becomes y=f(u) = u³, where u = 3x + 5
Using the above, please find the derivative of h(x) = f(g(x)) = (3x + 5)³ using:
Final Answer
a) Standard Form of Chain Rule:
[f(g(x)]' = f'(g(x)) g'(x)
b) Alternate Form of Chain Rule:
dy dy du
dx du dx
Final Answer
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