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Logarithmic differentiation

  1. Oct 23, 2006 #1
    1. ln x^(1/5)

    = 1/5 ln x which = 1/5 *1/x

    so overall it = 1/5x correct??

    Iam so lost on this problem.

    2. F(y) = y ln (1 + e^y)

    any help would be appreciated
     
  2. jcsd
  3. Oct 24, 2006 #2
    The first answer is correct. For the second, use the product rule.
     
  4. Oct 24, 2006 #3
    Alright thank you.. I have one more question though or some work to check to see if I did this correctly. Its on implicit differentiation:

    (x+y)^(1/2) = 1 + x^(2)y^(2)

    = 1/2 (x+y)^(-1/2) (1 + dy/dx) = x^(2) (2y dy/dx) + y^(2) (2x)

    = 1/2 (x+y)^(-1/2) - x^(2) - y^(2) (2x) = -(1 + dy/dx) + (2y dy/dx)

    I can get to this point but I dont know how to simplify to get me dy/dx.

    Iam not really sure how to get the dy/dx out of this -(1 + dy/dx) because its one term. Any help is apperciated. Thanks
     
  5. Oct 25, 2006 #4
    Expand the term on the left, and then gather all terms containing dy/dx.
     
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