  ZX-calculus has proved to be a useful tool for quantum technology with a wide
range of successful applications. Most of these applications are of an
algebraic nature. However, other tasks that involve differentiation and
integration remain unreachable with current ZX techniques. Here we elevate ZX
to an analytical perspective by realising differentiation and integration
entirely within the framework of ZX-calculus. We explicitly illustrate the new
analytic framework of ZX-calculus by applying it in context of quantum machine
learning for the analysis of barren plateaus.
