By far, the "freshman calculus" Superstar in economics is differentiation, because it is pervasive in all branches of the discipline, and at all levels, undergraduate post-graduate, PhD, professional academic.
And this is because, the core behavioral assumption in economics at the micro-level is that economic agents (persons, companies organizations, whatever), are all the time consciously and purposefully trying to optimize some measure, metric, whatever: utility, profit, value (maximization), cost, risk, loss (minimization)... in the world of economics, there is no such thing as "sit back and enjoy life", you are always on the look out (our agents, that is, inside our models), to ameliorate your position, in whatever way this "position" is represented -this is how you do enjoy life.
So we take derivatives as we breath, since, apart for special cases where the objective function may be constructed to be a bit weird, our functions are always differentiable -and even we have a model in discrete time, we find ways to do things similar to differentiation w.r.t time...
But I guess, what everybody knows about Economics is that the discipline has an obsession with the concept of "equilibrium", right? Well, watch us differentiate the equilibiurm condition of a model to obtain the relation between two variables of interest at the equilibrium point -and we are so used to it, some don't even know this is called the implicit function theorem.