Computing condition number of a polynomial root finding probelm

Question

Trefethen & Bau ("numerical linear algebra"; 1997) compute the condition number of polynomial root finding for $f(x) = (x-1)^2$ to be $k=\infty$ because the Jacobian does not exist. I want to know and understand the derivation of that result, because the book only explains it in words with an example perturbation of $x^2-2+0.9999 = (x-0.99)(x-1.01)$. Thank you.