To trigger the monostable shown here using the negative edge of a pulse, NOR gates are used. The delay is 0.7 x R x C [R in ohm and C in farad]. If the input remains unconnected to any circuit, add a pull-up resistor between 10 k ohm and 10 M ohm, depending on the application, to prevent erratic behavior. A recommended value for general applications is 100 k ohm.
Two NOR Gates Monostable