Since the unit step response of a network is given by the equation $1-e^{-αt}$, the unit impulse response of a network is the derivative of its unit step response. Therefore, we can find the unit impulse response by differentiating the given unit step response with respect to time (t).
Differentiating $1-e^{-αt}$ with respect to time (t):
$\frac{\mathrm{d} }{\mathrm{d} t}$ ($1-e^{-αt}$)
= 0 - $\frac{\mathrm{d} }{\mathrm{d} t}$ ($e^{-αt}$)
= 0 - (-α * $e^{-αt}$)
= α * $e^{-αt}$
Therefore, the correct answer to your question is Option A: α * $e^{-at}$
