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Math Help - finding the derivative of a definite integral

  1. #1
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    finding the derivative of a definite integral

    Find the derivative of the following function at x = 1




    Based on the Fundamental Theorem of Calculus, Part I would this be correct?



    Or would it become something like

    (-1+2t)/(1+2t)

    thanks, my teacher to so horrible. I might actually be able to learn something this way.
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  2. #2
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    y' = \frac{1 - x + x^2}{1+x+x^2} by Fundamental Theorem.

    To find y'(1) evaluate that function on RHS at 1.
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  3. #3
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    Quote Originally Posted by tehbrosta View Post
    Find the derivative of the following function at x = 1




    Based on the Fundamental Theorem of Calculus, Part I would this be correct?



    Or would it become something like

    (-1+2t)/(1+2t)

    thanks, my teacher to so horrible. I might actually be able to learn something this way.
    If

    y(x)=\int_0^x f(t) dt

    then the fundamental theorem tell us that:

    y'(x)=f(x)

    so:

    y'(1)=f(1)

    RonL
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  4. #4
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    So when I take the derivative at x=1 I get:

    y'(1) = (1-(1)+1^2)/(1+1+1^2) = 1/3?
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