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

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

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

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

2 x + 2 - 2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

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

= 2 x - 2 y + 0 + 2 - 0

Simplify

= 2 x + 2 - 2 y

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