I can't really think of anyone. Maybe just mathematicians, physicists, economists, computer scientists, chemists and engineers. Apparently they even use something called back propagation in AI training, which is nothing but chain rule from ... calculus.
But yeah, I can't see it being relevant since we have linear algebra already.
Geez, I don't know why I keep arguing with you people. I've seen several examples where just integrating or derivating something gets you an analytic solution that you can compute in an instant, rather than having to start doing some 3 dimension integrals numerically.
In every way you are referring to people using calculus in an applied sense always been reliant on linear algebra. Python libraries for doing backpropagation is built on numerical techniques that computes and is definitely not just manipulating symbols and calling it chain rule.
I am so glad that we are having an AI revolution within mathematics where hopefully the computability crowd will dethrone Cantorianist view.
You can just admit you don't understand calculus (and go and learn it if you care). No reason to go around doing mental gymnastics about it.