def deriv_η_skw_func(*, ρ, B_r, B_φ, B_θ, deriv_ρ, deriv_B_r, deriv_B_φ,
    deriv_B_θ):
    """
    Compute the scaled part of the derivative of η assuming the same form as in
    SKW
    """
    B_sq = B_r ** 2 + B_φ ** 2 + B_θ ** 2
    return (2 * (B_r * deriv_B_r + B_φ * deriv_B_φ + B_θ * deriv_B_θ) - 
        B_sq * deriv_ρ / ρ) / ρ
