Derivative equals inverse
The article presents a mathematical puzzle: finding a function f such that its derivative equals its inverse for all positive x. It describes this as an unusual differential equation that cannot be solved using standard techniques taught in typical differential equations classes.
Background
- This is a blog post by John D. Cook, a well-known mathematician and computer scientist who writes about applied math, statistics, and programming for a general technical audience. His blog often presents niche or elegant math puzzles in an accessible way.
- The post poses a functional equation: find a function whose derivative is equal to its own inverse function. This is not a standard differential equation problem — it blends calculus with the concept of an inverse function (the function that "undoes" the original, e.g., square root is the inverse of squaring).
- The problem is unusual because typical differential equations relate a function to its derivatives; here the relation involves the function's inverse, which makes standard techniques inapplicable. The interest lies in the clever trick or insight needed to solve it, not in a practical application.