Derivative Help

Discussion in 'Community Discussion' started by rhsgolfer33, Sep 16, 2009.

  1. rhsgolfer33 macrumors 6502a

    Joined:
    Jan 6, 2006
    #1
    So, I'm trying to find the derivative of f(x)=3/x. I know, using the power rule, that the derivative is -3x^-2 (or -3/x^2). However, I need to solve the problem using the f'(x)=[f(x+h)-f(x)]/h formula. Here is my work so far:

    f'(x)=[(3/x+h)-(3/x)
    Make common denominator of x(x+h)
    f'(x)=[3x/x(x+h)]-[(3(x+h))/x(x+h)]
    Simplify
    f'(x)=[3x/x(x+h)]-[(3x+3h)/x(x+h)]
    f'(x)=(3x-3x-3h)/x(x+h)
    f'(x)=-3h/x(x+h)

    That is where I loose it. I see that I can make the denominator (x^2)+hx, but that is about as far as I can get. Any help with this is appreciated. Its probably just my algebra failing me or a dumb mistake. Thanks for the help!
     
  2. swiftaw macrumors 603

    swiftaw

    Joined:
    Jan 31, 2005
    Location:
    Omaha, NE, USA
    #2
    You forgot the /h part in f'(x)

    f'(x)=limit as h-> of [(3/(x+h))-(3/x)]/h

    = [3x/x(x+h)]-[(3(x+h))/x(x+h)] / h

    = [-3h/x(x+h)] / h = -3 / (x^2 + xh)

    Now, as h-> 0, this becomes -3 / x^2
     
  3. rhsgolfer33 thread starter macrumors 6502a

    Joined:
    Jan 6, 2006
    #3
    Thank you! As I said, probably a dumb mistake, didn't think it would be that dumb! :eek:
     

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