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No-one seems to have answered the last question, the derivative of t*cos(t)
This just comes from the product rule. That is:
d/dt (f(t)*g(t)) = f'(t)*g(t) + f(t)*g'(t)
where f and g are functions in t, in this case let f(t) = t and g(t) = cos(t)
and f'(t) denotes the derivative of f(t), similarly for g(t). Hence in our case, f'(t) = d/dt (t) = 1, g'(t) = d/dt (cos(t)) = -sin(t)
So, d/dt t*cos(t) = cos(t) + t*(-sin(t)) = cos(t) - t*sin(t)
Sorry for trying to use so much math notation, so I hope it is clear.
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