What is (\partial)/(\partial x)(xe^x) ?

The answer to (\partial)/(\partial x)(xe^x) is e^x+e^xx

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(\partial)/(\partial x)(xe^x)

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

e^{x} + e^{x} x

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

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

Simplify

= e^{x} + e^{x} x

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What is (\partial)/(\partial x)(xe^x) ?
The answer to (\partial)/(\partial x)(xe^x) is e^x+e^xx