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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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