Question

Can't seem to get the right answer on this chain rule problem.

Answer 1

f(g(h(x))), where h(1) =2 , g(2)=2, h'(1)=8, g'(2)=-2, f'(2)=5. Find r'(1)

Answer 2

f'(g(h(x)))*(g'(h(x))*(h'(x)))

Answer 3

I don't see anything wrong with that.

Answer 4

but what is r(x)?

Answer 5

I see r' is asked about but no r

Answer 6

So, I plug in the numbers r(x)=f(g(h(x)))

Answer 7

ok so the thing you just found is r'
plug in 1 for x in r'

Answer 8

Once I plugged everything in I got (5)(2)*(-2(8)) = -160

Answer 9

hmmm... I got something a bit different let's go through it together

Answer 10

\[r'(x)=f'(g(h(x)))*(g'(h(x))*(h'(x))) \\ \text{ replace } x \text{ with } 1 \\ r'(1)=f'(g(h(1))) \cdot g'(h(1)) \cdot h'(1)\]
notice we know h(1) and h'(1)

Answer 11

\[r'(1)=f' (g(\color{red}{h(1)})) \cdot g'(\color{red}{h(1)}) \cdot \color{blue}{h'(1)}\]

Answer 12

replace these with the values given for h(1) and h'(1)

Answer 13

I still got the same thing because h(1) = 2 which makes g(2).

Answer 14

\[r'(x)=f'(g(h(x)))*(g'(h(x))*(h'(x))) \\ \text{ replace } x \text{ with } 1 \\ r'(1)=f'(g(h(1))) \cdot g'(h(1)) \cdot h'(1) \\ \]
\[r'(1)=f' (g(\color{red}{h(1)})) \cdot g'(\color{red}{h(1)}) \cdot \color{blue}{h'(1)}\]
we are given h(1) is 2 and h'(1) is 8
just plug them in... like this:
\[r'(1)=f' (g(\color{red}{2})) \cdot g'(\color{red}{2}) \cdot \color{blue}{8}\]

so now we have:
\[r'(1)=f'(g(2)) \cdot g'(2) \cdot 8 \\ r'(1)=f'(\color{red}{g(2)}) \cdot \color{blue}{g'(2)} \cdot 8\]
can you try to replace g(2) and g'(2) above?

Answer 15

(g(2))=2 and g'(2) = -2

So f'(2) =5
5*-2*8=-80
Is that correct?

Answer 16

yes good job

Answer 17

Thank you so much @freckles! I was just making a simple mistake.

Answer 18

k np