partial derivative

The operator \(\frac{\partial}{\partial x_{n}}\) takes the derivative of a function \(f(\vec{x})\) with respect to \(x_{n}\) in the direction of the \(x_{n}\) axis. In other words, we take the derivative \(f(\vec{x})\) as if all variables except \(x_{n}\) is constant; this is useful in cases where you only care about one variable.