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Derivative Help

  1. Nov 23, 2004 #1
    Hello all:

    I need help in finding the derivative of:

    log( sqrt(1+ log x) - sin x )

    I know that derivative of log x is 1/x.

    1/ sqrt(1 + logx) - sin x ) = sqrt(1+log x) + sin x / ( 1 + log x - sin ^2 x)

    Then I found derivative of inside expression and multiplied with the previous derivative. I get something almost the same as the answer, but I can't seem to simplify it.

    The answer is:

    (1- 2x)* sqrt(1 + log x cos x) / 2x * sqrt(1 + log x)* sqrt(1 + log x - sin x)

    Any help is greatly appreciated

    Thanks!
     
  2. jcsd
  3. Nov 23, 2004 #2
    Using the chain rule, if you make u = (sqrt(1+logx) - sinx), then the derivative will be
    1/u * du/dx, where du/dx is:
    1/2sqrt(1+logx) * 1/x - cosx

    I hope this will help. When you are derivating sqrt(1+logx), you have to use again the cahin rule, so it will be sqrt(v), and the derivative will be:
    1/2sqrt(v) * v´
     
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