or partial differential coefficient, n. the derivative of a function of two or more variables with respect to one of these variables, the others being regarded as constant; written Higher partial derivatives arise as partial derivatives of partial derivatives. If different variables are used in the repeated process a mixed partial derivative arises. Thus, is a mixed second partial derivative, which is the result of differentiating the partial derivative ∂ f/∂ y with respect to x. In general, the order of the derivative is the number of times the given function is differentiated. The ambiguity about the sequence in which the derivatives are taken is removed when the partial derivatives of that order are continuous around the point; then the order is irrelevant, and, for example, f_xxy=f_xyx. Compare total derivative.