1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Quotient Rule
  1. Quotient rule (Replies: 6)

  2. Quotient Rule (Replies: 14)