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Methods for determining derivatives of f(x) between grid points for linear interpolation. Top: An example of f(x) and the interpolation function F(x). Bottom: The derivative df/dx provided by central finite difference of f(x). which only exists at the grid points. Also shown are (a) dF/dx the derivative of the interpolation function F(x) and (b) the linear interpolation of df/dx. Method (b) is more accurate at the grid points with respect to the central finite difference.
