This problem is a very simple example of a differential equation: an equation that relates a function to one or more of its derivatives. You can solve this problem by doing some educated guessing. ("educated" means "remember what we did in the past.") Suppose ff is the function that satisfies f′(x)=−f2(x) f′(x)=−f2(x) for all xx in its domain, and f(1)=1.