def partial_velocity(vel_list, u_list, frame):
    """Returns a list of partial velocities.

    For a list of velocity or angular velocity vectors the partial derivatives
    with respect to the supplied generalized speeds are computed, in the
    specified ReferenceFrame.

    The output is a list of lists. The outer list has a number of elements
    equal to the number of supplied velocity vectors. The inner lists are, for
    each velocity vector, the partial derivatives of that velocity vector with
    respect to the generalized speeds supplied.

    Parameters
    ==========

    vel_list : list
        List of velocities of Point's and angular velocities of ReferenceFrame's
    u_list : list
        List of independent generalized speeds.
    frame : ReferenceFrame
        The ReferenceFrame the partial derivatives are going to be taken in.

    Examples
    ========

    >>> from sympy.physics.mechanics import Point, ReferenceFrame
    >>> from sympy.physics.mechanics import dynamicsymbols
    >>> from sympy.physics.mechanics import partial_velocity
    >>> u = dynamicsymbols('u')
    >>> N = ReferenceFrame('N')
    >>> P = Point('P')
    >>> P.set_vel(N, u * N.x)
    >>> vel_list = [P.vel(N)]
    >>> u_list = [u]
    >>> partial_velocity(vel_list, u_list, N)
    [[N.x]]

    """
    if not hasattr(vel_list, '__iter__'):
        raise TypeError('Provide velocities in an iterable')
    if not hasattr(u_list, '__iter__'):
        raise TypeError('Provide speeds in an iterable')
    list_of_pvlists = []
    for i in vel_list:
        pvlist = []
        for j in u_list:
            vel = i.diff(j, frame)
            pvlist += [vel]
        list_of_pvlists += [pvlist]
    return list_of_pvlists