@staticmethod
def fit_deriv(x, amplitude, x_0, alpha, x_cutoff):
    'One dimensional exponential cutoff power law derivative with respect to parameters'
    xx = (x / x_0)
    xc = (x / x_cutoff)
    d_amplitude = ((xx ** (- alpha)) * np.exp((- xc)))
    d_x_0 = (((alpha * amplitude) * d_amplitude) / x_0)
    d_alpha = (((- amplitude) * d_amplitude) * np.log(xx))
    d_x_cutoff = (((amplitude * x) * d_amplitude) / (x_cutoff ** 2))
    return [d_amplitude, d_x_0, d_alpha, d_x_cutoff]
One dimensional exponential cutoff power law derivative with respect to parameters
@staticmethod
def fit_deriv(x, amplitude, x_0, alpha, x_cutoff):
    
    xx = (x / x_0)
    xc = (x / x_cutoff)
    d_amplitude = ((xx ** (- alpha)) * np.exp((- xc)))
    d_x_0 = (((alpha * amplitude) * d_amplitude) / x_0)
    d_alpha = (((- amplitude) * d_amplitude) * np.log(xx))
    d_x_cutoff = (((amplitude * x) * d_amplitude) / (x_cutoff ** 2))
    return [d_amplitude, d_x_0, d_alpha, d_x_cutoff]