@staticmethod
def fit_deriv(x, amplitude, x_0, alpha):
    'One dimensional power law derivative with respect to parameters'
    xx = (x / x_0)
    d_amplitude = (xx ** (- alpha))
    d_x_0 = (((amplitude * alpha) * d_amplitude) / x_0)
    d_alpha = (((- amplitude) * d_amplitude) * np.log(xx))
    return [d_amplitude, d_x_0, d_alpha]
One dimensional power law derivative with respect to parameters
@staticmethod
def fit_deriv(x, amplitude, x_0, alpha):
    
    xx = (x / x_0)
    d_amplitude = (xx ** (- alpha))
    d_x_0 = (((amplitude * alpha) * d_amplitude) / x_0)
    d_alpha = (((- amplitude) * d_amplitude) * np.log(xx))
    return [d_amplitude, d_x_0, d_alpha]