What is (\partial)/(\partial x)(xe^x+2e^xy) ?

The answer to (\partial)/(\partial x)(xe^x+2e^xy) is e^x+e^xx+2ye^x

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(\partial)/(\partial x)(xe^x+2e^xy)

\frac{\partial}{\partial x} (x e^{x} + 2 e^{x} y)

e^{x} + e^{x} x + 2 y e^{x}

Solution steps

\frac{\partial}{\partial x} (x e^{x} + 2 e^{x} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 e^{x} y) = 2 y e^{x}

= e^{x} + e^{x} x + 2 y e^{x}

What is (\partial)/(\partial x)(xe^x+2e^xy) ?
The answer to (\partial)/(\partial x)(xe^x+2e^xy) is e^x+e^xx+2ye^x