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

[krzyeghts8888]

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

 

[Cyosis]

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?

 

[krzyeghts8888]

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

 

[Cyosis]

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.