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What does it mean that the response of the system to the derivative of the input signal is equal to the derivative of the input signal response? What's the role?
Meaning: If the input signal is X and the system output signal is f(x), then f(x')=f'(x).
The function is that if the response f(x) of the system is known, then the response of the derivative of the input signal is also known, so it is not necessary to bring x' in, and just take the derivative of f(x) directly.