Suppose I have a quadratic (weighted) least-square fit result obtained from a given set of data:
$$ f(x) = \underbrace{-0.243(\pm0.3324)}_{\text{quad}_a}x^2\underbrace{{}-0.921(\pm0.061)}_{\text{quad}_b}x \underbrace{{}-2.12(\pm0.0223)}_{\text{quad}_c} $$ If I'm taking the derivative of $f(x)$ to have $f'(x) = Ax+B$, I wonder how can I figure out the uncertainties on $A$ and $B$? I also have the correlations
C(quad_a, quad_c) = -0.422
C(quad_a, quad_b) = -0.278
Thanks!