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

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

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

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

2 x + y - 2

Solution steps

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

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

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

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

= 2 x + y + 0 - 2 + 0

Simplify

= 2 x + y - 2

\frac{( s )}{s ^{2} + 5 s + 6}

\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

\frac{d y}{d x} + 10 y = 8

\int_{1}^{5} x^{3} - 5 x^{2} - x + 5 d x

\frac{d}{d y} (2 1 - y^{2} - (\frac{x}{4})^{2})

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