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

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

x^{2} - 4 x y + x \frac{d y}{d x} = 0

\int x^{\frac{- 5}{3}} d x

x^{^{'}} = 2 - x

y^{^{''}} + y = sin (t)

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