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Homework Help: Diffrentiation of natural logs (ln)

  1. Sep 14, 2010 #1
    the question is: differentiate wiith repsect to x:

    (ln(5x))^1/5

    i differentiated and got :

    1/5ln(5x)

    y'=1/5x


    I dont think this is correct. The answer should be ln5/5.

    Can anyone help me?

    chanella
     
  2. jcsd
  3. Sep 14, 2010 #2
    That's not right. The answer shouldn't be ln5/5, because that's a number. The answer should be a function.

    Use the chain rule: power to the front, subtract 1, multiply by the derivative of what's inside the bracket.
     
  4. Sep 14, 2010 #3
    So the answer would be;

    y'=1/5 (5)(ln5x)^(1/5-1)

    y'= (ln5x)^-4/5

    is this right??

    Thanks for helping :)
     
  5. Sep 14, 2010 #4
    Almost. The derivative of ln(f(x)) is f'(x)/f(x), so the derivative of ln(5x) is 5/(5x) = 1/x.

    So replacing (5) with (1/x), then simplifying is the correct answer.
     
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