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

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

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

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

2 x + 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{3}) = 0

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

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

= 0 + 2 x + 2 y

Simplify

= 2 x + 2 y

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