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Homework Help: Find derivative of y. y= ln (1 + √x) / (x^3)

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi guys, I've got :

    [tex] y= ln ( (1 + √x) / x^{3})[/tex]

    2. The attempt at a solution
    I honestly don't know where to go from here, I tried getting the ln of each of them.

    [tex]y = ln 1 +ln√x - ln x^{3} [/tex]

    Am I doing it write? If not, how am I suppose to work this problem out? If so, where do I go from here?
  2. jcsd
  3. Oct 24, 2012 #2


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    Education Advisor

    First note, log(1+sqrt(x)) does not equal log(1) + log (sqrt(x)). You're thinking about this property:

    log(ab) = log(a) + log(b). So, what you should have is this mess below:

    [itex] y = \ln{(1+\sqrt{x})} - \ln{x^3} [/itex]

    On the first part, use the chain rule, on the second part use the chain rule. Show your work and we'll see where you go astray.
  4. Oct 24, 2012 #3
    O.K. so I started doing the chain rule for the first one and got:

    [tex] (1/(1 + √x) )(1/(2√x) ) [/tex]

    Is it right so far?

    EDIT: I did the second one and got:

    [tex] (1/(x^{3}) ) (3x^{2} )[/tex]
    Last edited: Oct 24, 2012
  5. Oct 24, 2012 #4
    ok I got used the chain rule and got

    [tex] [(1/2x^{-1/2})/(1 + √x)] - [(3x^2)/(x^3)] [/tex]


    [tex] 1/[ (2√x) + 2x ] - 3/x [/tex]

    How do I go from here to get the answer :

    [tex](-6 -5√x)/[2x(1 + √x) ] [/tex] ?
  6. Oct 24, 2012 #5


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    Find a common denominator & combine fractions.
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