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Find dy/dx of y=(cosx)^x

  1. Dec 15, 2011 #1
    1. The problem statement, all variables and given/known data

    Find dy/dx of y=(cosx)^x

    2. Relevant equations

    d/dx of a^u=lna*a^u*u'

    3. The attempt at a solution

    I thougt I just had to follow the form shown above, and this is what I got.

    y=(cosx)^x
    dy/dx=ln(cosx)*(cosx)^x*1
    dy/dx=ln(cosx)*(cosx)^x

    However, the actual answer is (cosx)^x*(ln(cosx)-xtanx)
    I don't understand where this comes from at all. Thanks for your input.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 15, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    That's not a good form to follow. It assumes that in a^u that a is a constant. That isn't true in your case. Try writing v^u=e^(log(v)*u) and differentiate that.
     
  4. Dec 17, 2011 #3
    ln y = x ln cosx

    You can now use the product rule on the right side..
    (Hint: it becomes (1/y)y' on the left)
     
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