'One dimensional Lorentzian model derivative with respect to parameters'

@staticmethod
def fit_deriv(x, amplitude, x_0, fwhm):

    d_amplitude = ((fwhm ** 2) / ((fwhm ** 2) + ((x - x_0) ** 2)))
    d_x_0 = (((amplitude * d_amplitude) * ((2 * x) - (2 * x_0))) / ((fwhm ** 2) + ((x - x_0) ** 2)))
    d_fwhm = ((((2 * amplitude) * d_amplitude) / fwhm) * (1 - d_amplitude))
    return [d_amplitude, d_x_0, d_fwhm]
