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Calculus 1 chain rule

  1. Dec 25, 2013 #1
    I'm not entirely sure if this belongs in homework or elsewhere -- I'm self-teaching working through a basic calculus text, so it's not homework per se. In any case it's a simple differentiation problem wherein I am supposed to differentiate:

    f(x) = x(3x-9)^3
    f'(x) = 3x(3)(3x-9)^2 Applying chain rule
    f'(x) = 9x(3x-9)^2

    I know this isn't the correct answer.

    I was half tempted to multiply out using the binomial theorem but I suspect there's a more efficient way to solve this. How am I to treat the x coefficient? Evidently not as a constant.
     
  2. jcsd
  3. Dec 25, 2013 #2
    Did you see the product rule?

    [tex](fg)^\prime = f^\prime g + fg^\prime[/tex]
     
  4. Dec 25, 2013 #3

    HallsofIvy

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    You have to use the product rule first, then the chain rule.

    Of, since [itex]x= (x^{1/3})^3[/tex], f(x)= (x^{1/3}(3x- 9))^3= (3x^{4/3}- 9x^{1/3})^3
    and now use the chain rule.
     
  5. Dec 26, 2013 #4

    NascentOxygen

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    There, itex fixed. :wink:
     
  6. Dec 26, 2013 #5

    HallsofIvy

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    Thanks!:redface:
     
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