'One dimensional Moffat model derivative with respect to parameters'

@staticmethod
def fit_deriv(x, amplitude, x_0, gamma, alpha):

    d_A = ((1 + (((x - x_0) ** 2) / (gamma ** 2))) ** (- alpha))
    d_x_0 = (((((- amplitude) * alpha) * d_A) * (((-2) * x) + (2 * x_0))) / ((gamma ** 2) * (d_A ** alpha)))
    d_gamma = (((((2 * amplitude) * alpha) * d_A) * ((x - x_0) ** 2)) / ((gamma ** 3) * (d_A ** alpha)))
    d_alpha = (((- amplitude) * d_A) * np.log((1 + (((x - x_0) ** 2) / (gamma ** 2)))))
    return [d_A, d_x_0, d_gamma, d_alpha]
