Consider I can find the step response of a system with the following method:
We can easily find the step input of a system from its transfer function. Given a system with input $x(t)$, output $y(t)$ and transfer function $H(s)$
$$H(s) = \frac{Y(s)}{X(s)}$$
the output with zero initial conditions (i.e., the zero state output) is simply given by
$$Y(s) = H(s)X(s)$$
so the unit step response, $Y_\gamma(s)$, is given by
$$ Y_\gamma(s) = \frac{1}{s} H(s) $$
If my input is a "differentiating system" then what will be the step response ?