Question

Given a unit step function u (t), its time-derivative is:

(a) A unit impulse

(b) Another step function

(c) A unit ramp function

(d) A sine function

The question was posed to me in unit test.

This interesting question is from The z- and s-Domain Relationship topic in division Digital Control Systems of Control Systems

Answer 1

Right choice is (a) A unit impulse

The best I can explain: Unit step function is one of the test signals and for the basic standard signals they are interrelated as the function of differentiation and integration as unit step function is the integral of impulse function.