  We prove that the speed of $\lambda$-biased random walks on a supercritical
Galton-Watson tree without leaves is differentiable when $\lambda\in(0,1)$, and
give an expression of the derivative using a certain 2-dimensional Gaussian
random variable. The proof heavily uses the renewal structure of Galton-Watson
trees that was introduced by Lyons-Pemantle-Peres.

Probability