When both parameters are set to $1$, the differential equation for logistic population growth is $$x'=x(1-x)$$
Suppose the population is also harvested at the constant rate $h$. The differential equation then apparently becomes $$x'=x(1-x)-h$$
Here's what I don't understand: If the population is harvested at the constant rate $h$, it means that $x$ is reduced by $h$ periodically. Why would this also mean that $x'$ is reduced by $h$?