Hmm...How would you evaluate the LHS? I thought the RHS matrix could be simplified further to arrive at something that resembles the LHS :-)Uhh... what you have is the RHS of the question.
What you need to do is take the LHS of the question, evaluate it, and show that it is equal to what you just wrote (aka the RHS of the question).
Thank you Mark and I.L.SThe left side is the derivative of the cross product u(t) X v(t). Calculate the cross product, and then take the derivative. If that turns out to be equal to what you have in post #24, you have shown that d/dt(u(t) X v(t)) = u'(t) X v(t) + u(t) X v'(t).