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Math Help - Finding equation of line tangent to curve

  1. #1
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    Finding equation of line tangent to curve

    seem to have a problem with basic differentiation:

    Question: y = 1/(x^2 + 1)
    At point x = 1, y = 1/2

    Work:
    (x^2+1)^-1
    -1(X^2+1)^-2 (2x)
    (-x^2-1)^-2 (2x)
    (-(1)^2 - 1)^-2(2(1)

    however, 1 - 1 = 0 and applying ^2 means you are dividing two by zero? where did I go wrong, thanks.
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  2. #2
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    Re: Finding equation of line tangent to curve

    Two problems: You changed -1(x^2+1)^{-2} to (-x^2-1)^{-2}, which is not correct, and when you plugged in x=1 to -x^2, you multiplied by -1 first and then squared, which again is not correct.

    The correct answer is:
    -1(x^2+1)^{-2} (2x) = -\frac{2x}{(x^2+1)^2} = -\frac{2}{(1+1)^2} = -\frac{1}{2}

    - Hollywood
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  3. #3
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    Re: Finding equation of line tangent to curve

    but (1+1)^2 = 4? oh nm... ofc when I really look at it I see after posting
    Last edited by togo; January 23rd 2013 at 08:37 AM.
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