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If the input-output relationship is given by y(t) = 2x(t) ^d⁄dx x(t). What kind of system it represents?

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in Signals and Systems by (1.2m points)
If the input-output relationship is given by y(t) = 2x(t) ^d⁄dx x(t). What kind of system it represents?

(a) Linear system

(b) Non linear system

(c) LTI system

(d) Linear but time-invariant system

The question was posed to me during an interview.

My doubt is from Properties of Systems topic in portion Signals and Systems Basics of Signals and Systems

1 Answer

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by (42.1k points)
Right option is (b) Non linear system

Easy explanation: The given input-output relationship of the system does not satisfy the principle of superposition theorem hence it is an example for non linear system.

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