A derivada da função t cos(t) é
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![\frac{d}{dt}[f(t)g(t)] = f(t) \frac{d}{dt}[g(t)] + g(t) \frac{d}{dt}[f(t)] \frac{d}{dt}[f(t)g(t)] = f(t) \frac{d}{dt}[g(t)] + g(t) \frac{d}{dt}[f(t)]](https://tex.z-dn.net/?f=+%5Cfrac%7Bd%7D%7Bdt%7D%5Bf%28t%29g%28t%29%5D+%3D+f%28t%29+%5Cfrac%7Bd%7D%7Bdt%7D%5Bg%28t%29%5D+%2B+g%28t%29+%5Cfrac%7Bd%7D%7Bdt%7D%5Bf%28t%29%5D+++)
![\frac{d}{dt}[ t \cos(t)] = t \frac{d}{dt}[\cos(t)] + \cos(t) \frac{d}{dt}[ t] \frac{d}{dt}[ t \cos(t)] = t \frac{d}{dt}[\cos(t)] + \cos(t) \frac{d}{dt}[ t]](https://tex.z-dn.net/?f=+%5Cfrac%7Bd%7D%7Bdt%7D%5B+t+%5Ccos%28t%29%5D+%3D+t+%5Cfrac%7Bd%7D%7Bdt%7D%5B%5Ccos%28t%29%5D+%2B+%5Ccos%28t%29+%5Cfrac%7Bd%7D%7Bdt%7D%5B+t%5D+)
![\frac{d}{dt} [t \cos(t) ]= -t \sin(t) + \cos(t) \frac{d}{dt} [t \cos(t) ]= -t \sin(t) + \cos(t)](https://tex.z-dn.net/?f=+%5Cfrac%7Bd%7D%7Bdt%7D+%5Bt+%5Ccos%28t%29+%5D%3D+-t+%5Csin%28t%29+%2B+%5Ccos%28t%29+)
![\frac{d}{dt} [t \cos(t) ]= \cos(t) - t \sin(t) \frac{d}{dt} [t \cos(t) ]= \cos(t) - t \sin(t)](https://tex.z-dn.net/?f=+%5Cfrac%7Bd%7D%7Bdt%7D+%5Bt+%5Ccos%28t%29+%5D%3D+%5Ccos%28t%29+-+t+%5Csin%28t%29+)
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