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

  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. LCKurtz

    LCKurtz 8,447
    Homework Helper
    Gold Member

    Your work is correct. You could be slightly less ambiguous with parentheses though.
  4. Thanks.
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