# Thread: finding the derivative of a definite integral

1. ## 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

$\displaystyle (-1+2t)/(1+2t)$

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

2. $\displaystyle y' = \frac{1 - x + x^2}{1+x+x^2}$ by Fundamental Theorem.

To find $\displaystyle y'(1)$ evaluate that function on RHS at 1.

3. Originally Posted by tehbrosta
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

$\displaystyle (-1+2t)/(1+2t)$

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

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

then the fundamental theorem tell us that:

$\displaystyle y'(x)=f(x)$

so:

$\displaystyle y'(1)=f(1)$

RonL

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

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