y(t) = u(t) * h(t) (always)
where h(t) is impulse response
∵ s(t) step response (given)
⇒ ddts(t) = h(t)
∴ y(t) = u(t) * ddts(t)
= ddt[u(t) * s(t)] (using property)
= ddt ∫∞−∞ u(τ) s(t-τ) dτ
(by definition of convolution)
= ddt∫t0 u(τ) s(t-τ)dτ
(∵ u(t) and s(t) are causal functions)