tmagloire1
  • tmagloire1
ap calc ab help http://prntscr.com/8grqwg
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
tmagloire1
  • tmagloire1
@misty1212
Jhannybean
  • Jhannybean
\[\frac{d}{dx}(g(f(x))) = g'(f(x)) \cdot f'(x)\]
misty1212
  • misty1212
HI!!

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misty1212
  • misty1212
and hi @Jhannybean !!
Jhannybean
  • Jhannybean
Hi!!! @misty1212
tmagloire1
  • tmagloire1
Hi everyone xD Thanks for helping me!!
misty1212
  • misty1212
you have all the numbers you need to plug in to what @Jhannybean wrote above plug them in, see what you get
tmagloire1
  • tmagloire1
Wait so I understand how to plug in the f(x) and f'(x) but how do I do the g(x) and g'(x)
misty1212
  • misty1212
let me just add one little bit \[\frac{d}{dx}(g(f(3x))) = g'(f(3x)) \cdot f'(3x)\cdot 3\]
Jhannybean
  • Jhannybean
So now we have \(g'(f(x)) \cdot f'(x)\) take it one step at a time. \[g'(f(1)) \cdot f'(1)=~?\]
misty1212
  • misty1212
careful a little it is \(f(3x)\) so at \(x=1\) it is \(f(3)\)
Jhannybean
  • Jhannybean
Oooo stupid me. I misread a portion of the problem.
Jhannybean
  • Jhannybean
Yeah. Just noticed.
tmagloire1
  • tmagloire1
So if x=1 at f(3x) = f(3) what am i supposed to use to plug in.. im actually really confused
misty1212
  • misty1212
now got to read them off of the table at \(x=1\) it is \[g'(f(3)) \cdot f'(3)\cdot 3\]
misty1212
  • misty1212
what is \(f'(3)\) from the table?
tmagloire1
  • tmagloire1
2
tmagloire1
  • tmagloire1
i mean 10
Jhannybean
  • Jhannybean
and what is \(f(3)\) from the table?
tmagloire1
  • tmagloire1
2
misty1212
  • misty1212
and finally, what is \(g'(2)\)?
tmagloire1
  • tmagloire1
5
tmagloire1
  • tmagloire1
So would it be 5(10)(3)=150?
Jhannybean
  • Jhannybean
Yeah
misty1212
  • misty1212
number therapy for learning the chain rule
tmagloire1
  • tmagloire1
Haha thank you so much! Okay so would that be how you do it at x=1 or is that just an example from the chart?
Jhannybean
  • Jhannybean
We did it at x=1
tmagloire1
  • tmagloire1
Oh okay i understand so we just broke it up into components
tmagloire1
  • tmagloire1
Thank you so much both of you for your help!!
Jhannybean
  • Jhannybean
\[g'(f(1))\cdot f'(1) = \\ g'(f(3(1))) \cdot f'(3(1)) \cdot 3 = \\ g'(f(3)) \cdot f'(3) \cdot 3 = \\ g'(2) \cdot 10\cdot 3 = \\ 5 \cdot 10\cdot 3 = 150\]

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