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Help finding a derivative.

  1. Sep 18, 2006 #1
    Hello. I have been trying to find this derivative from first principles for at least a couple hours, but just can't make any progress with it.

    Find the derivative of [tex]3x-\frac{5}{x}[/tex]

    Well I start by saying that the derivative is the limit as h approaches 0 of

    [tex]\frac{f(x+h)-f(x)}{h} [/tex] where h=deltax

    Then I go on to say that this is equal to the limit as h approaches 0 of
    [tex]\frac{3h-\frac{5}{x+h}+\frac{5}{x}}{h} [/tex]

    I then simplify by taking h out of the numerator by factoring and then cancel h on the numerator and denominator. This the derivative equals the limit as h approches 0 of
    [tex]3-\frac{5}{(x+h)h}+\frac{5}{xh} [/tex]

    As you can see, my derivative is now a bloody mess and I see no way of getting h out of the denominator. Please help! By the way I need to do this from first principles (dy/dx=(f(x+h)-f(x))/(h) ). Thankyou! :surprised
    Last edited: Sep 18, 2006
  2. jcsd
  3. Sep 18, 2006 #2
    The last term in the numrator is [tex]\frac{5}{x}[/tex].
  4. Sep 18, 2006 #3
    try combining the fractions into:
    [tex]\frac{-5x+5(x+h)}{(x+h)hx} [/tex]
    EDIT: can't seem to get that latex to work... anyone see where I went wrong with it?
    Last edited: Sep 18, 2006
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