SOLUTION: Let F(x)=f(x^5) and G(x)=(f(x))^5. You also know that a^4=10,f(a)=3, f′(a)=3,f′(a^5)=8. Find F′(a) and G'(a). I know that derivative of x^5 is 5x^4, but I d

Algebra ->  Linear-equations -> SOLUTION: Let F(x)=f(x^5) and G(x)=(f(x))^5. You also know that a^4=10,f(a)=3, f′(a)=3,f′(a^5)=8. Find F′(a) and G'(a). I know that derivative of x^5 is 5x^4, but I d      Log On


   

Question 1110067: Let F(x)=f(x^5) and G(x)=(f(x))^5. You also know that a^4=10,f(a)=3,
f′(a)=3,f′(a^5)=8.
Find F′(a) and G'(a).
I know that derivative of x^5 is 5x^4, but I don't know where to start. Please help!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
F(x) = f(x5)

Using the chain rule:

F'(x) = f'(x5)∙5x4

F'(a) = f'(a5)∙5a4

F'(a) = 8∙5∙10

F'(a) = 400

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G(x) = [f(x)]5

Using the chain rule:

G'(x) = 5∙[f(x)]4∙f'(x)

G'(a) = 5∙[f(a)]4∙f'(a)

G'(a) = 5∙34∙3

G'(a) = 1215

Edwin