f(t) = real-valued function
u(t) = vector
I need help to prove the following:
d/dt [f(t)u(t)] = f'(t)u(t) + f(t)u'(t)
I know this is probably easy for you guys, but I haven't had a clue what I am doing for 4+ years now, so if this thing delves into some crazy series summation or something I am prob gonna cry.
I saw the proof for the dot product of two vectors, but I cannot do it here as I don't think I know what to do when a function is multiplied by a parametrization, I would assume you just parametrize the vector and then go from there, but I don't know what that would look like in a proof, or maybe treat the function as a scalar... sorry idk what I am talking about.