What is (\partial)/(\partial t)(te^t+2) ?

The answer to (\partial)/(\partial t)(te^t+2) is e^tt+e^t

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(\partial)/(\partial t)(te^t+2)

\frac{\partial}{\partial t} (t e^{t} + 2)

e^{t} t + e^{t}

Solution steps

\frac{\partial}{\partial t} (t e^{t} + 2)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial t} (t e^{t}) + \frac{\partial}{\partial t} (2)

\frac{\partial}{\partial t} (t e^{t}) = e^{t} + e^{t} t

\frac{\partial}{\partial t} (2) = 0

= e^{t} + e^{t} t + 0

Simplify

= e^{t} t + e^{t}

What is (\partial)/(\partial t)(te^t+2) ?
The answer to (\partial)/(\partial t)(te^t+2) is e^tt+e^t