Question

Let f and g be the functions in the table below.

(a) If F(x) = f(f(x)), find F '(1).

(b) If G(x) = g(g(x)), find G'(3).

Any idea on what to do here?

Answer 1

The chain rule :)
\[\Large F(x) = f(f(x)) \implies F'(x) = f'(f(x))\cdot f'(x)\]

Answer 2

I'll do the F, you do the G.
The process is identical.

Sound good? :)

Answer 3

Yeah, sounds good. Thank you

Answer 4

First of all, you do recall the chain rule?
(In general here it is:)
\[\Large \frac{d}{dx}f[g(x)]= f'[g(x)]\cdot g'(x)\]

Answer 5

So...
This follows
\[\Large F(x) = f(f(x)) \implies F'(x) = f'(f(x))\cdot f'(x)\]

Answer 6

Therefore:
\[\Large F'(1) = f'(\color{red}{f(1)})\cdot f'(1)\]

Answer 7

So, first of all, what is f(1) ?

Answer 8

3

Answer 9

That's right :)
So replace f(1) with 3:
\[\Large F'(1) = f'(\color{red}{3})\cdot f'(1)\]
Next, what is f'(3) ?

Answer 10

7

Answer 11

Right again :)
So we replace f'(3) with 7
\[\Large F'(1) = \color{red}{7}\cdot f'(1)\]
Finally, what is f'(1) ?

Answer 12

4

Answer 13

\[\Large F'(1) = \color{red}{7}\cdot \color{green}{4}\]
That wasn't too bad, now was it? ^_^

Answer 14

28. Thank you I think I kinda get it. I'll try to do the next one

Answer 15

Please :)
And post your answer :D

Answer 16

6*9=54?

Answer 17

bravo :)

Answer 18

Wow. Thanks so much for the help!

Answer 19

No problem :)