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

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

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = e^{t}

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

\frac{\partial}{\partial t} (t) = 1

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

= 1 \cdot e^{t} + e^{t} t

Simplify

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

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