dx1dy
dx1dy is a shorthand notation used in calculus to represent the partial derivative of a function with respect to a variable, and then the partial derivative of that result with respect to another variable. More specifically, it denotes the second-order partial derivative.
The notation is a compact way of writing the mixed partial derivative. If we have a function
In many cases, for functions that are sufficiently smooth (specifically, if the second partial derivatives are
The dx1dy notation is particularly useful in contexts such as differential equations and advanced physics where