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As an example, if you want to take the derivative of:

d/dt [ r(t) X r'(t)]

I just used the general rule of d/dt [r1(t) X r2(t)] = r1(t)Xr2'(t) + r1'(t)Xr2(t)

I ***thought**** I was doing the problem correctly but apparently not.

I just did the following by using the generic equation above:

d/dt [ r(t) X r'(t)] = r(t)Xr''(t) + r'(t)Xr'(t)

What is wrong with what I did? At the back of my book it says the answer is r(t) Xr''(t) which is the first part of my answer (but doesn't include the second portion). Can someone explain where I'm wrong? I'd really appreciate it.