Question

Help please??

Answer 1

Oh this is kind of a fun little exercise :)
Chain rule time!

Answer 2

If h(x) = f(f(x))

what is h'(x)=?

Answer 3

I don't know because whats the value of f? Is it 1?

Answer 4

no no don't look at the chart yet :O
just apply your chain rule.

if y = g(x)

then y' = g'(x)
yes?

Answer 5

But here we have a `composition of functions`,
so they're testing your understanding of the chain rule.

Answer 6

Our chain rule tells us that if \(\large\rm y=f(g(x))\) then \(\large\rm y'=f'(g(x))\cdot g'(x)\).

Remember that?
You take the derivative of the outer function `f in the example`
and multiply by the derivative of the inner function `g in the example`

Answer 7

Oh okay thats right so its f'(f(x)

Answer 8

you took the derivative of the outer function, good.
but you didn't multiply by the derivative of the inner function

Answer 9

So I would multiply it by f'(x)?

Answer 10

good good good.
so when \(\large\rm h(x)=f(f(x))\) we have found that \(\large\rm h'(x)=f'(f(x))\cdot f'(x)\)

Answer 11

And NOWWWW you can use your chart :)

Answer 12

\[\large\rm h'(\color{orangered}{x})=f'(f(\color{orangered}{x}))\cdot f'(\color{orangered}{x})\]So we want h'(1), yes?\[\large\rm h'(\color{orangered}{1})=f'(f(\color{orangered}{1}))\cdot f'(\color{orangered}{1})\]

Answer 13

And then I would get 18 correct?

Answer 14

Oh I thought we just plug in the values for 1

Answer 15

It's going to be kind of tricky following the chart here!
Let's start from the inner most function.
See that f(1) on the inside?
What does that value give us?

Answer 16

\[\large\rm h'(1)=f'(\color{red}{f(1)})\cdot f'(1)\]So this is what we're working on first, this red part.

Answer 17

Thats going to be 3 right?

Answer 18

\[\large\rm h'(1)=f'(\color{red}{3})\cdot f'(1)\]Good good.

Answer 19

And then would you multiply it be by 2 since thats the f'(1)

Answer 20

\[\large\rm h'(1)=f'(3)\cdot 2\]2 for f'(1)?
Yup sounds good! :)
Getting so close!

Answer 21

So then I would have 6 and I would multiply that by 7?

Answer 22

No no no silly.
The 3 can't multiply the 2.
The 3 is the argument of the function, he can't be messed with.

Look up f'(3) on your chart. No multiply just yet! :O

Answer 23

F'(3)=7

Answer 24

\[\large\rm h'(1)=7\cdot 2\]Mmmm good! :3

Answer 25

So 14 would be the final answer?

Answer 26

yayyyy good job \c:/

Answer 27

Okay thank you very much!

Answer 28

nppp