Here, $\lambda(y_0)$ denotes the Lyapunov exponent of the logistic orbit starting at $y_0$.
I tried starting like this: We have $F(x_k)=ax_k(1-x_k)$. Hence $|F'(x_k)|=|a-2a x_k|$, but I have no idea how to compute $$\lambda(x_0)= \lim_{n \to \infty} \frac{1}{n} \sum_{i=0}^{n-1} \ln | F'(x_i)|.$$