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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

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

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

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


    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


    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


    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
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