Dado f(t) = (e^3t sen t, 3t - 2) , calcule f ' (t) :

Sendo \(f(t) = (e^{3t} \sin t \,\,, \,\, 3t-2 )\), a derivada \(f'(t)\) é:

\(\Longrightarrow f'(t) = \Big ((e^{3t} \sin t)' \,\,, \, \,(3t-2)' \Big)\)

\(\Longrightarrow f'(t) = \Big ((e^{3t})' \sin t + e^{3t} (\sin t)' \,\,, \, \,(3t)'-(2)' \Big )\)

\(\Longrightarrow f'(t) = \Big (3e^{3t} \sin t + e^{3t} \cos t \,\,, \, \,3-0 \Big )\)

\(\Longrightarrow \fbox {$ f'(t) = \Big (e^{3t} (3\sin t + \cos t) \,\,, \, \,3 \Big) $}\)

Dado f(t) = (e^3t sen t, 3t - 2) , calcule f ' (t) :