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!

Find the derivative of the function(Quotient rule)

  1. Feb 14, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the derivative of the function

    [itex]
    y = (3-2x^3+x^6 )/x^9
    [/itex]
    2. Relevant equations
    Derivatives

    3. The attempt at a solution
    I have tried to use the quotient rule

    and got to
    [itex]
    -6x^11 + 6x^14 - 27x^8 + 18x ^24 - 9x ^14 / (x^9)^2
    [/itex]
    Which doesn't look close to the answer
    [itex]
    -27/x^10 + 12/x^7 - 3 / x^4
    [/itex]
     
  2. jcsd
  3. Feb 14, 2016 #2

    fresh_42

    Staff: Mentor

    Can you type in the steps to see what you have done so far? And you can as well use the product rule, it's the same.
    I assume you have calculated ##(-9)(-2x^3)x^{8} = 18x^{24}## which is wrong. It has to be ##18x^{11}##.
     
    Last edited: Feb 14, 2016
  4. Feb 14, 2016 #3
    1st Part

    (-6x^2+6x^5)(x^9) - ( 3-2x^3 + x^6) (9x^8)

    2nd Part

    -6x^11 + 6x^14 - (27x^8 - 18x^24 + 9x^14)

    3rd Part

    -6x^11+6x^14 - 27x^8 + 18x^24-9x^14

    lol its hard to type math with itex
    finished posting.
     
  5. Feb 14, 2016 #4

    fresh_42

    Staff: Mentor

    See my editorial above: ##x^3 \cdot x^8 = x^{11}## not ##x^{24}##.
     
  6. Feb 14, 2016 #5
    Ah I see, I changed it up and it seems closer to the answer, but how do you transform from

    (-27x^8+12x^11 - 3x^14)/ ((x^9)^2)

    to( what do we do to the denominator)

    -27/x^10 + 12/ x^7 - 3/ x^4

    which is the answer
     
  7. Feb 14, 2016 #6

    fresh_42

    Staff: Mentor

    ##(x^9)^2 = x^{18}## and ##\frac{1}{x^{18}}=x^{-18}##. So for example the first term is ## -27x^8 \cdot x^{-18}= -27x^{-10}=\frac{-27}{x^{10}}##.
     
  8. Feb 14, 2016 #7
    lol I never woulda thought it that far
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted