This is a self-made problem. I have a function $A$ of variables $x, m \geq 0$. A satisfies the following symmetry:
$$A(x, m) = 1 - A(m, x)$$
Is there an equation that relates the partial derivative of $A$ wrt the first argument to the partial derivative of $A$ with respect to the second argument? It seems like there should be something straightforward but I'm not sure how to deduce it.