The derivative of a constant is zero, so G(s) remains 2/(s+2) and d/dx(8) remains 0.
(a) G(s) = 2/(s + 2):
This system represents a first-order system with a single pole at -2.
When a unit step input is applied (representing a sudden jump from 0 to 1 at t=0), the output will initially rise exponentially towards its steady-state value.
However, because the derivative of a constant (here, the 2 in the numerator) is zero, the system settles at the steady-state value of 2 immediately without any further rise.
Therefore, the output remains constant at 2 after the step input.
(b) 8 = 10/(x + 5):
This is not a system in the typical sense but an algebraic expression.
The expression itself does not change over time, regardless of any input.
Applying a unit step input has no effect, as the expression only depends on the variable x, not on time.
Therefore, the output remains constant at 8 at all times.
In essence, both systems react to the unit step input by quickly reaching their respective constant values due to the lack of any internal dynamics (in system (a)) or time dependence (in expression (b)).