This problem is an 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. Suppose f is the function that satisfies for all z in its domain, and f'(x) = (x) f(1) = 1. Then f(z) = Hint: try some of your familiar functions: parabolas, hyperbolas, exponential, trig, power functions.