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Finding the derivative of a function.

  1. Oct 23, 2012 #1
    Differentiate:



    y = 4 8√x^2


    Attempt to solve the problem.

    f ' (x) = 4(x^2/8)

    f ' (x) = 4 ( (2/8) x ^-6/8)

    f ' (x) = 4 ( (2/8) χ 1/x ^ 6/8)

    f ' (x) = 4 ( 2/ x^6)

    f ' (x) = 8/x ^ 6

    I have no idea if this is the right answer, due to the fact that this is an online multiple choice question for homework, and I would have to pick none of the above. Problem is, I have been "none of the above" for every question so far, and I'm thinking I'm doing fundamentally wrong, even though I don't see it. Any help would be appreciated.
     
    Last edited: Oct 23, 2012
  2. jcsd
  3. Oct 23, 2012 #2
    The way you wrote this is a little confusing. Is the problem written:

    [itex] y = 4 \sqrt[8]{x^{2}} [/itex]

    ?
     
  4. Oct 23, 2012 #3
    Yes, sorry for the confusion.
     
  5. Oct 23, 2012 #4
    Ok, no worries. Then we have:

    [itex] f(x) = 4 x^{\frac{2}{8}} = 4 x^{\frac{1}{4}} [/itex]

    [itex] f'(x) = \frac{1}{4} 4 x^{\frac{-3}{4}} [/itex]

    [itex] f'(x) = \frac{1}{x^{\frac{3}{4}}} [/itex]

    It doesn't have to be written this exact way though, so it's up to you to figure out if one of the options is correct. Also, the mistake you made was that you dropped the 8 in the denominator between the 3rd and 4th steps.
     
  6. Oct 23, 2012 #5
    f ' (x) = 4 ( (2/8) χ 1/x ^ 6/8)

    f ' (x) = 4 ( 2/ x^6)

    To clarify where you mistake was, remember that the 2nd 8 is in the exponent, so it's not part of the fractions you were multiplying. The second step here should have been:

    [itex] f'(x) = 4(\frac{2}{8 x^{\frac{6}{8}}}) [/itex]

    Then you could reduce further and have the correct answer.
     
  7. Oct 23, 2012 #6
    I see, thank you very much! That makes much more sense now.
     
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