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How to differentiate x^(cosx) = y^(sinx) with respect to x

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Differentiate x^(cosx) = y ^(sinx) with respect to x

    2. Relevant equations



    3. The attempt at a solution
    I tried using natural logs but im not sure if its correct, if it's wrong please point me to the right direction, thanks

    x^(cosx) = y^(sinx)
    ln x^(cosx) = ln y ^(sinx)
    ln x (cosx) = ln y (sinx)
    cosx/x - sinx lnx = cosx lny +sinx/y (dy/dx)
    cosx/x - sinx lnx - cosx lny = sinx/y (dy/dx)
    (cosx/x - sinx lnx - cosx lny) / (sinx/y) = dy/dx
     
  2. jcsd
  3. Apr 18, 2012 #2

    LCKurtz

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    Homework Helper
    Gold Member

    Your work is correct. You could be slightly less ambiguous with parentheses though.
     
  4. Apr 18, 2012 #3
    Thanks.
     
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