How Do You Correctly Apply the Chain Rule to Find Derivatives F'(a) and G'(a)?

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Homework Help Overview

The problem involves finding the derivatives F'(a) and G'(a) for the functions F(x) = f(x^8) and G(x) = (f(x))^8, given specific values for f and its derivatives at a particular point.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the chain rule to both functions, with one participant providing calculations for G'(a) and F'(a). There is uncertainty about the correctness of these calculations, particularly regarding the introduction of a constant 'k' in the derivative of F.

Discussion Status

The discussion is ongoing, with participants questioning the validity of the attempts and the presence of the constant 'k'. There is a call for clarification on the application of the chain rule, particularly for F'(a), suggesting that further exploration of the problem is needed.

Contextual Notes

Participants are working under the assumption that the provided values for f and its derivatives are accurate, but there is a lack of clarity regarding the role of the constant 'k' in the context of the problem.

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Homework Statement



Let F(x)= f(x^8) and G(x)=(f(x))^8. You also know that a^7= 14, f(a)=2, f'(a)= 10, f'(a^8)=4 Find F'(a)=______ and G'(a)=______


Homework Equations





The Attempt at a Solution



G(a)=(f(a))^8
G'(a)=8(f(a))^7*(f'(a))
G'(a)=8(2)^7*10
G'(a)=10240

F(a)=f(a^8)
F'(a)=k(f'(a))
F'(a)=1*(4)
F'(a)=4

One of the two is incorrect but I do not know which one and I am am not sure how to go about finding it
 
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Sorry for being suspicious, but are these your own attempts at a solution? I find it hard to believe that you can do one correctly and completely miss the other. What is k?
 
Cyosis said:
Sorry for being suspicious, but are these your own attempts at a solution? I find it hard to believe that you can do one correctly and completely miss the other. What is k?

Yes they're my own attempts. The reason I don't know why I'm missing one of them is cause I don't see anything wrong! Which is why I'm looking for help. And k is the sign for constant
 
How does that constant end up there? There is not a single k to be found anywhere else in your problem. Either way apply the chain rule in the same way as you did with G.
 
Last edited:

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