When derivative equals inverse

Is there a function whose derivative is its inverse? In other words, is there a function f that satisfies f ‘(x) = f-1(x) for positive x? Indeed there is one given here. Let φ be the golden ratio (√5 + 1)/2. Then for x > 0 the function f(x) = φ (x/φ)φ satisfies our equation. […] The post When derivative equals inverse first appeared on John D. Cook....

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