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F(g(x)) chain rule help

  • Thread starter fiziksfun
  • Start date
  • #1
78
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ok so f(g(x)) = x, for all x.

f(3)=8
f'(3)=9

what are the values of g(8) and g'(8)

ok, so g(8) = 3

because f(g(8)) must equal 8, and f(3) = 8, so g(x) must equal three.

however, i have NO idea how to do g'(x)

i was thinking of using the chain rule, but this gets me nowhere..help!!

f'(g(x))*g'(x) = 8 ?? is this correct?? then wouldnt g'(x) = 1 ??
 
Last edited:

Answers and Replies

  • #2
Vid
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chain rule
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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ok so f(g(x)) = x, for all x.

f(3)=8
f'(3)=9

what are the values of g(8) and g'(8)

ok, so g(8) = 3

because f(g(8)) must equal 8, and f(3) = 8, so g(x) must equal three.

however, i have NO idea how to do g'(x)

i was thinking of using the product rule, but this gets me nowhere..help!!

f'(g(x))*g'(x) = 8 ?? is this correct?? then wouldnt g'(x) = 1 ??
chain rule
What fiziksfun wrote in his last line is the chain rule, not the product rule.
If (f(g(x))= x then f'(g(x))*g'(x)= (x)'= 1, not 8.
 
  • #4
78
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the chain rule doesn't get me anywhere :[
 
  • #5
78
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how do you know (x)' is equal to 1 ???
 
  • #6
Vid
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Yea, I saw product rule in his post and just skipped over the symbols.
 
  • #7
78
0
oh wait, is it because d/dx(x) = 1 ?? YAY!!
 
  • #8
HallsofIvy
Science Advisor
Homework Helper
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924
Wow, that was fast!

I must admit that when you asked how I knew that the derivative of x was 1, I started to reach for my 2 by 4!
 

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