What is (\partial)/(\partial y)(x^3y+e^x) ?

The answer to (\partial)/(\partial y)(x^3y+e^x) is x^3

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(\partial)/(\partial y)(x^3y+e^x)

\frac{\partial}{\partial y} (x^{3} y + e^{x})

x^{3}

Solution steps

\frac{\partial}{\partial y} (x^{3} y + e^{x})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{3} y) + \frac{\partial}{\partial y} (e^{x})

\frac{\partial}{\partial y} (x^{3} y) = x^{3}

\frac{\partial}{\partial y} (e^{x}) = 0

= x^{3} + 0

Simplify

= x^{3}

x^{^{'}} = x^{\frac{4}{5}}

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What is (\partial)/(\partial y)(x^3y+e^x) ?
The answer to (\partial)/(\partial y)(x^3y+e^x) is x^3