def METHOD_NAME(self, use_exp=False):
    """
    The derivative of the kernel w.r.t. time.
    """
    if use_exp:
        val = - self.ec[1] * self.c0 * self.e[self.c_slice]
    else:
        zz = nm.zeros(self.c[0:1].shape, dtype=self.c.dtype)
        val = nm.r_[nm.diff(self.c, axis=0) /
                    nm.diff(self.times, axis=0)[self.c_slice], zz]
    return val