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

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

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

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

x + 2 y

Solution steps

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

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

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

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

= 0 + x + 2 y

Simplify

= x + 2 y

10 - 7 x, y = 0, x^{2} - 20

\int 2 x + 3 x^{- 2} d x

\int \frac{5 sin ^{3} ( x )}{x} d x

\frac{d y}{d t} + 2 y = 3 e^{t}, y (0) = 1

y = ln (x^{4})

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