Trisarahtops
  • Trisarahtops
Use the table below to evaluate d/dx [g[f(2x]] at x=1. x 1 2 3 4 f(x) 6 1 8 2 f ′(x) 1 3 5 7 g(x) 1 4 4 3 g ′(x) 4 5 5 –4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
Use the table below to evaluate d/dx [g[f(2x)] at x=1. \(\bf ~~x \quad \quad~ 1\quad \quad~ 2\quad ~~~3\quad~~~4\) `f(x) 6 1 8 2` f ′(x) 1 3 5 7 `g(x) 1 4 4 3` g ′(x) 4 5 5 –4 making it more clear
SolomonZelman
  • SolomonZelman
Apply the chain rule to differentiate the g.
Trisarahtops
  • Trisarahtops
wait don't we have to set it up fiirst

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SolomonZelman
  • SolomonZelman
you already have the set up
SolomonZelman
  • SolomonZelman
You need to evaluate g'(1) .... no?
SolomonZelman
  • SolomonZelman
Isn't that the meaning of evaluating the derivative (d/dx) of g(x) at x=1??
SolomonZelman
  • SolomonZelman
So do you agree that you need g'(1) ?
Trisarahtops
  • Trisarahtops
uh I guess not sure. Idk i'm just confused on how to start
SolomonZelman
  • SolomonZelman
The derivative of \(\color{#000000 }{ \displaystyle f(x) }\) is \(\color{#0000ff }{ \displaystyle f'(x) }\). However, if you have a function of \(x\) inside the \(f(x)\), then The derivative of \(\color{#000000 }{ \displaystyle f(g(x)) }\) is NOT just \(\color{#ff0000}{ \displaystyle f'(g(x)) }\). Rather, the derivative of \(\color{#000000 }{ \displaystyle f(g(x)) }\) is (YES) \(\color{#0000ff }{ \displaystyle f'(g(x))\cdot g'(x) }\), and we get this by applying the Chain Rule. And what happens when you have another function of x inside the g(x)- (in your case "2x"), you apply the chain rule once again. The derivative of \(\color{#000000 }{ \displaystyle f(g(2x)) }\) is NOT \(\color{#ff0000 }{ \displaystyle f'(g(2x))\cdot g'(2x) }\); Rather, the derivative of \(\color{#000000 }{ \displaystyle f(g(2x)) }\) is \(\color{#0000ff }{ \displaystyle f'(g(2x))\times g'(2x) \times 2 }\)
SolomonZelman
  • SolomonZelman
I might have said in a too lengthy way, but I just want to make sure you understand that the chain rule is applied multiple times.
Trisarahtops
  • Trisarahtops
no no this makes more sense to me. so since x=1 it's just f'(g(2)) x g'(2) x 2
SolomonZelman
  • SolomonZelman
yes, very good
Trisarahtops
  • Trisarahtops
so now i plug in what's in the chart
SolomonZelman
  • SolomonZelman
yes
Trisarahtops
  • Trisarahtops
f'(4)) x 5 x 2 7 x 10 70
SolomonZelman
  • SolomonZelman
Yes, fabulous !!
Trisarahtops
  • Trisarahtops
Thank you so much ;)
SolomonZelman
  • SolomonZelman
Anytime!
ayeedomo
  • ayeedomo
It's domo! :D
SolomonZelman
  • SolomonZelman
domo?
ayeedomo
  • ayeedomo
domo icon
Trisarahtops
  • Trisarahtops
yup. someone in a domo suit ;D
ayeedomo
  • ayeedomo
lol
SolomonZelman
  • SolomonZelman
.... \( ; ) \)

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