Boundary derivative of a chordal Loewner chain
= Boundary derivative of a chordal Loewner chain
For a real $x$ before its swallowing time,
$$
g_t'(x)=\exp\left(
-\int_0^t\frac{2\,ds}{(g_s(x)-U_s)^2}\right).
$$
It lies in $(0,1]$ and decreases with time.