Does there exist a monotonically decreasing function that is its own derivative?

$f(x) = -ce^x, c > 0$

This isn't a particularly exciting answer, but it is the correct one. All functions that are their own derivatives are of the form $f(x) = ce^x, c \in \mathbb{R}$, as explained in this question: Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$

Tags:

Calculus

Derivatives

Real Analysis

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