Find a nonzero function such that f′ (x) = 4f (x)

One nonzero function that satisfies f′ (x) = 4f (x) can be found by using the constant 'e' and its derivative rules. If we define f (x) = e^ (4x), the first derivative f' (x) can be found via the chain rule to be 4*e^ (4x) or the 4*f (x) as desired.