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Homework Help: Quotient Rule

  1. Jan 31, 2008 #1
    1. The problem statement, all variables and given/known data
    Find f '(x) two ways: By using the product or quotient rule, and by simplifying first.
    f(x) = ((x^3) + 9)/ (x^3)

    2. Relevant equations
    f '(x)= (G(x) * F '(x) - F(x) * G '(x)) / [G(x)^2]

    3. The attempt at a solution
    f '(x)= (x^3)(3x^2) - (x^3 + 9)(3x^2) / (x^3)^2 Plug into quotient rule
    f '(x)= (3x^5) - (3x^5) - (27x^2) / (x^6) Simplify
    f '(x)= (-27x^2)/(x^6) Canceled out 3x^5
    f '(x)= (-27)/ (x^4) Simplified exponents

    The answer in the back of the book is what I have(f '(x)= -27/(x^4) =-27x^-4)

    So am I done? Was I supposed to simplify from the original equation for f(x) also? I guess I'm asking what "simplify first" exactly means. Any help is greatly appreciated, thank you!
  2. jcsd
  3. Jan 31, 2008 #2
    simplify first probably means,

    f(x) = (x^3 + 9)/x^3 = 1 + 9/x^3 = 1 + 9x^(-3),
    so f'(x) = -27x^(-4)
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