# What is the derivative of #f(t) = (tcos^2t , t^2-cost ) #?

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The derivative of ( f(t) = (t\cos^2(t), t^2 - \cos(t)) ) with respect to ( t ) is:

[ f'(t) = \left( \frac{d}{dt} (t\cos^2(t)), \frac{d}{dt} (t^2 - \cos(t)) \right) ]

[ f'(t) = \left( \cos^2(t) - 2t\sin(t)\cos(t), 2t + \sin(t) \right) ]

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