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

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

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

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

3 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

= 3 x y^{2} + 0

Simplify

= 3 x y^{2}

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