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Derivative of Logarithm with trig

  1. Jun 18, 2014 #1
    Need to find derivative

    y = θ(sin(ln θ)) + cos(ln θ)


    My work

    θ(cos(ln θ))(1/θ) + sin(ln θ) + (-sin(ln θ)(1/θ))

    (θcos(ln θ))/θ] + sin(ln θ) + ( (- sin(ln θ))/θ)

    cos(ln θ) + [θsin(ln θ) - sin(ln θ)]/ θ

    answer in book is 2cos(lnθ)
     
  2. jcsd
  3. Jun 18, 2014 #2

    Ray Vickson

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    Your answer is correct, and the book's answer is wrong. Are you sure you copied the problem correctly?
     
  4. Jun 18, 2014 #3
    Yeah it is correct
     
  5. Jun 18, 2014 #4
    I propose that it was supposed to be
    \begin{equation*}
    y(\theta) = \theta(\sin(\ln \theta) + \cos(\ln \theta)).
    \end{equation*}
     
  6. Jun 18, 2014 #5

    Ray Vickson

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    As Quesadilla points out, the function ##f(\theta) = \theta ( \sin(\ln \theta) + \cos(\ln \theta))## is probably what you want; its derivative agrees with the book's answer.
     
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