def _sabr_implied_vol_hagan_A11_fprime_by_strike(underlying, strike,
    maturity, alpha, beta, rho, nu):
    """_sabr_implied_vol_hagan_A11_fprime_by_strike
    See :py:func:`_sabr_implied_vol_hagan_A11`.

    :param float underlying:
    :param float strike:
    :param float maturity:
    :param float alpha: must be within :math:`[0, 1]`.
    :param float beta: must be greater than 0.
    :param float rho: must be within :math:`[-1, 1]`.
    :param float nu: volatility of volatility. This must be positive.

    :return: value of factor.
    :rtype: float.
    """
    one_minus_beta_half = (1.0 - beta) / 2.0
    one_plus_beta_half = (1.0 + beta) / 2.0
    factor = one_minus_beta_half * underlying ** one_minus_beta_half
    return factor * strike ** -one_plus_beta_half
