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Derivative of a fraction

  1. Nov 14, 2014 #1
    I am new to this forum, i don't know if it's here i should post this simple question.
    I have to find the peak of the function:
    ##\frac{x}{\sqrt{x^2+R^2}(x^2+R^2)}=\frac{x}{(x^2+R^2)^{3/2}}##
    I differentiate:
    ##\left( \frac{x}{(x^2+R^2)^{3/2}} \right)'=\frac{(x^2+R^2)^{3/2}+x\left( \frac{3}{2}(x^2+R^2)^{3\2}\cdot 2x \right)}{(x^2+R^2)^3}##
    Only the numerator:
    ##(x^2+R^2)^{1/2}\left[ (x^2+R^2)^3+3x^2 \right]##
    When i equal it to 0 i get, as one possibility:
    ##(x^2+R^2)^3=-3x^2##
    And it's not good, since x has a value.
     
  2. jcsd
  3. Nov 14, 2014 #2

    Mentallic

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    Homework Helper

    You've factorized incorrectly here.

    Also, your derivative is incorrect. Remember u'v - v'u, as opposed to +.
     
    Last edited: Nov 14, 2014
  4. Nov 14, 2014 #3
    Thanks
     
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