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f(x) + f'(x) puzzle

Enter a trial function f(x) that can depend on up to two parameters a and b. The goal is to find a function such that the sum of the function and its derivative vanishes for all x. If both x and f(x) are quantities rather than numbers [see "Semantic Aspects of Quantity" on the mathMINDhabits website] explain how and why f(x) and f'(x) can be added.