I examine the role of Hamiltonians in economics pedagogy and practice. Hamiltonians are often introduced in economics problems in order to avoid functional differentiation of functionals that depend on the time derivative of the control variables. Unfortunately, constructing a Hamiltonian from a Lagrangian requires one to do this anyway, so in teaching Hamiltonians tend to be magicked out of nowhere. In doing this, important topics such as Legendre transforms and constrained Hamiltonian dynamics are passed over. On the other hand, it is very easy to introduce the topic of functional differentiation in a practical way, that does not require any knowledge beyond `normal' calculus. I provide such an introduction in section 2. Therefore, Lagrangian dynamics can easily be taught in a self-contained fashion that deals with constraints in a much more transparent fashion, and that is entirely sufficient for economics applications. I believe this approach could notably improve economics pedagogy.