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Homework Help: Derivative of cos(x)^(x+7)

  1. Mar 3, 2010 #1
    Help! I haven't the slightest clue on how to do this...

    thanks in advance!
     
  2. jcsd
  3. Mar 3, 2010 #2
    [tex]y=cos^{x+7}(x)[/tex]

    Start by taking the natural logarithmic of both sides.
     
  4. Mar 3, 2010 #3
    even the y?

    so i'd have:

    ln(y) = (x+7)ln(cos(x))

    how do i get rid of the ln on the y?

    cause i knew it was a ln problem, just i dont know how to get rid of the ln on the y
     
  5. Mar 3, 2010 #4
    Don't worry about 'getting rid of the ln' yet. The problem is about taking derivatives, so take one and see what happens.
     
  6. Mar 4, 2010 #5

    Mark44

    Staff: Mentor

    If you take the derivative of the left side, you should get (1/y)(dy/dx). On the right side, you should have the derivative of ((x + 7)ln(cos x)). Solve the resulting equation for dy/dx.
     
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