feat(analysis/calculus/uniform_limits_deriv): Swap limits and derivatives (#14090)
This commit proves that the derivative of the pointwise limit of a series of functions is the limit of the derivatives when the derivatives converge uniformly in some closed ball.
This and #13500 are two fundamental theorems for bootstrapping the theory of Dirichlet series. This theory underlies my ongoing attempts to prove the density of squarefree integers.