Derivative equals inverse

🫧 Open on Bubbles Here’s kind of a strange problem with an interesting solution: find a function f such that the derivative of f equals the inverse of f for all positive x . f ′( x ) = f −1 ( x ) This is a differential equation, but a very unusual one, one that cannot be solved using any of the techniques taught in a class on differential equations. The unique solution is f ( x ) = φ( x / φ) φ where φ is the golden ratio. What an unexpected appearance of the golden ratio! The problem was proposed by H. L. N