'One dimensional log parabola derivative with respect to parameters'

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

    xx = (x / x_0)
    log_xx = np.log(xx)
    exponent = ((- alpha) - (beta * log_xx))
    d_amplitude = (xx ** exponent)
    d_beta = (((- amplitude) * d_amplitude) * (log_xx ** 2))
    d_x_0 = ((amplitude * d_amplitude) * (((beta * log_xx) / x_0) - (exponent / x_0)))
    d_alpha = (((- amplitude) * d_amplitude) * log_xx)
    return [d_amplitude, d_x_0, d_alpha, d_beta]
