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Derivative Quesiton

  1. Oct 24, 2006 #1
    find the derivative of the following:
    f(x) = x/(x+c/x)

    through simplication, i got:
    =x(x^-1 + c^-1*x)

    taking the derivative,
    -c^-2*x^2 + c^-1*2x

    its wrong though so where did i go wrong?
  2. jcsd
  3. Oct 24, 2006 #2
    That's not right. (x+y)-1 is not the same as x-1 + y-1.

    Without simplifying the original expression you could have used the quotient rule to find the derivative, OR you could differentiate x(x+cx^-1)^-1 using the product rule.
  4. Oct 25, 2006 #3


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    Staff Emeritus
    Science Advisor

    I would be inclined to multiply both numerator and denominator of the function by x:
    [tex]f(x)= \frac{x}{x+ \frac{c}{x}}= \frac{x^2}{x^2+ c}[/tex]
    for all x except 0.
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