What is (\partial)/(\partial y)(x^3y+e^{xy^2}) ?

The answer to (\partial)/(\partial y)(x^3y+e^{xy^2}) is x^3+e^{xy^2}*2xy

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(\partial)/(\partial y)(x^3y+e^{xy^2})

\frac{\partial}{\partial y} (x^{3} y + e^{x y^{2}})

x^{3} + e^{x y^{2}} \cdot 2 x y

Solution steps

\frac{\partial}{\partial y} (x^{3} y + e^{x y^{2}})

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 y^{2}})

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

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

= x^{3} + e^{x y^{2}} \cdot 2 x y

What is (\partial)/(\partial y)(x^3y+e^{xy^2}) ?
The answer to (\partial)/(\partial y)(x^3y+e^{xy^2}) is x^3+e^{xy^2}*2xy