'Two dimensional Moffat model derivative with respect to parameters'

@staticmethod
def fit_deriv(x, y, amplitude, x_0, y_0, gamma, alpha):

    rr_gg = ((((x - x_0) ** 2) + ((y - y_0) ** 2)) / (gamma ** 2))
    d_A = ((1 + rr_gg) ** (- alpha))
    d_x_0 = (((((- amplitude) * alpha) * d_A) * (((-2) * x) + (2 * x_0))) / ((gamma ** 2) * (1 + rr_gg)))
    d_y_0 = (((((- amplitude) * alpha) * d_A) * (((-2) * y) + (2 * y_0))) / ((gamma ** 2) * (1 + rr_gg)))
    d_alpha = (((- amplitude) * d_A) * np.log((1 + rr_gg)))
    d_gamma = ((((2 * amplitude) * alpha) * d_A) * (rr_gg / (gamma * (1 + rr_gg))))
    return [d_A, d_x_0, d_y_0, d_gamma, d_alpha]
