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tmagloire1

  • one year ago

ap calc ab help http://prntscr.com/8grqwg

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  1. tmagloire1
    • one year ago
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    @misty1212

  2. Jhannybean
    • one year ago
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    \[\frac{d}{dx}(g(f(x))) = g'(f(x)) \cdot f'(x)\]

  3. misty1212
    • one year ago
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    HI!!

  4. misty1212
    • one year ago
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    and hi @Jhannybean !!

  5. Jhannybean
    • one year ago
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    Hi!!! @misty1212

  6. tmagloire1
    • one year ago
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    Hi everyone xD Thanks for helping me!!

  7. misty1212
    • one year ago
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    you have all the numbers you need to plug in to what @Jhannybean wrote above plug them in, see what you get

  8. tmagloire1
    • one year ago
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    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)

  9. misty1212
    • one year ago
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    let me just add one little bit \[\frac{d}{dx}(g(f(3x))) = g'(f(3x)) \cdot f'(3x)\cdot 3\]

  10. Jhannybean
    • one year ago
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    So now we have \(g'(f(x)) \cdot f'(x)\) take it one step at a time. \[g'(f(1)) \cdot f'(1)=~?\]

  11. misty1212
    • one year ago
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    careful a little it is \(f(3x)\) so at \(x=1\) it is \(f(3)\)

  12. Jhannybean
    • one year ago
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    Oooo stupid me. I misread a portion of the problem.

  13. Jhannybean
    • one year ago
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    Yeah. Just noticed.

  14. tmagloire1
    • one year ago
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    So if x=1 at f(3x) = f(3) what am i supposed to use to plug in.. im actually really confused

  15. misty1212
    • one year ago
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    now got to read them off of the table at \(x=1\) it is \[g'(f(3)) \cdot f'(3)\cdot 3\]

  16. misty1212
    • one year ago
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    what is \(f'(3)\) from the table?

  17. tmagloire1
    • one year ago
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    2

  18. tmagloire1
    • one year ago
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    i mean 10

  19. Jhannybean
    • one year ago
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    and what is \(f(3)\) from the table?

  20. tmagloire1
    • one year ago
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    2

  21. misty1212
    • one year ago
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    and finally, what is \(g'(2)\)?

  22. tmagloire1
    • one year ago
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    5

  23. tmagloire1
    • one year ago
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    So would it be 5(10)(3)=150?

  24. Jhannybean
    • one year ago
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    Yeah

  25. misty1212
    • one year ago
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    number therapy for learning the chain rule

  26. tmagloire1
    • one year ago
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    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?

  27. Jhannybean
    • one year ago
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    We did it at x=1

  28. tmagloire1
    • one year ago
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    Oh okay i understand so we just broke it up into components

  29. tmagloire1
    • one year ago
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    Thank you so much both of you for your help!!

  30. Jhannybean
    • one year ago
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    \[g'(f(1))\cdot f'(1) = \\ g'(f(3(1))) \cdot f'(3(1)) \cdot 3 = \\ g'(f(3)) \cdot f'(3) \cdot 3 = \\ g'(2) \cdot 10\cdot 3 = \\ 5 \cdot 10\cdot 3 = 150\]

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