def _evaluate_cubic_spline_derivative_one(x, y, r, t):
    """Evaluate one point on the first derivative of the cubic spline.

    Parameters:
        x : rank-1 np.array of np.float64, length 2
            data x coordinates
        y : rank-1 np.array of np.float64, length 2
            data y coordinates
        r : rank-1 np.array of np.float64, length 2
            corresponding elements of output of solve_coeffs() for your data
        t : float
            point where to evaluate. Must be between the given x values.

    Returns:
        s : float
            Value of the derivative at the point t.
"""
    h = x[1] - x[0]
    a = -2 * ( y[1] - y[0] ) + (   r[0] + r[1] ) * h
    b =  3 * ( y[1] - y[0] ) - ( 2*r[0] + r[1] ) * h
    c = r[0] * h

    lt = (t - x[0]) / h  # 0..1
    return ((3*a*lt + 2*b) * lt + c)/h