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Let F(x)=f(f(x)) and G(x)= F(x)^2

f(3)=5, f(5)=3, f'(3)=6, f'(5)=8

Find: F'(3) and G'(3)

I found F'(3) to equal 48...but I was unsure of how to find G'(3).

Another similar problem that I'm having trouble with is:

F(x)=f(x^9) and G(x)=((f(x))^9). You also know that a^8=6, f(a)=3, f'(a)=12, f'(a^9)=9

Find F'(a) and G'(a)...I have no idea how to do either of those, if you could please help I'd really appreciate it.
 
amanda8991 said:
Let F(x)=f(f(x)) and G(x)= F(x)^2

f(3)=5, f(5)=3, f'(3)=6, f'(5)=8

Find: F'(3) and G'(3)

I found F'(3) to equal 48...but I was unsure of how to find G'(3).

Another similar problem that I'm having trouble with is:

F(x)=f(x^9) and G(x)=((f(x))^9). You also know that a^8=6, f(a)=3, f'(a)=12, f'(a^9)=9

Find F'(a) and G'(a)...I have no idea how to do either of those, if you could please help I'd really appreciate it.
Click to expand...


F'(3) does equal 48.

G(x)=(F(x))^2

using power and chain rules

G'(x)=2F(x)F'(x)


For the second problem

F(x)=f(x^9)

so

F'(x)=(9x^8)f'(x^9)

also

G(x)=(f(x))^9

so G'(x)=9(f(x))^8 (f'(x))
 
Use the chain rule.

\(\displaystyle F'(x)=f'(x)f'(f(x))\)

\(\displaystyle G'(x)=2F(x)F'(x)=2f(f(x))f'(x)f'(f(x))\)

Hope I write that correctly :wink:
 
No, look more carefully. It won't be that big. You have F'(x)=48, you know it's

multiplied by 2. What is F(x)?. Multiply by that and you have it. (48)(2)(?)=?
 
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