Along a differentiable path of fields , a differentiable functional obeysIntegrating in time expresses the functional change as the line integral of its functional derivative along the path.
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The concept of a functional derivative is a generalization of the ordinary derivative to functionals, which are mappings from a space of functions to the real numbers (or complex numbers). In essence, while a regular derivative gives the rate of change of a function with respect to its variables, a functional derivative captures the rate of change of a functional with respect to changes in the function it depends on.