They give a differential equation: [itex] x' = f_a(x) = ax(1-x) [/itex]. In determining if the equilibrium points are sources or sinks, they say: We may also determine this information analytically. We have [itex] f'_a(x) = a - 2ax [/itex] How can they differentiate with respect to x? x is a function, it doesn't represent a point on the real line. I tried assuming that they really mean [itex] x'(t) = f_a(x(t)) = ax(t)(1 - x(t)) [/itex], but that would mean that [itex] x''(t) = f'_a(x(t)) = ax'(t) - 2ax(t)x'(t) [/itex], which according to the book is wrong. What's going on here?