Vector in orbital theory.

Hi,

I need help with the following equations.

n = r/r (unit vector in r direction)


v =d r/dt = dr/dt n + r dn/dt



L = r X (mv) = mr^2 [n X (dn/dt)]

how did this
mr^2 [n X (dn/dt)]
came about?

I would expect some thing from
r X (mv)
to this
m (v X r)