What is (\partial)/(\partial x)(x^2+2xy+2y^2-6x+10y+2) ?

The answer to (\partial)/(\partial x)(x^2+2xy+2y^2-6x+10y+2) is 2x+2y-6

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(\partial)/(\partial x)(x^2+2xy+2y^2-6x+10y+2)

\frac{\partial}{\partial x} (x^{2} + 2 x y + 2 y^{2} - 6 x + 10 y + 2)

2 x + 2 y - 6

Solution steps

\frac{\partial}{\partial x} (x^{2} + 2 x y + 2 y^{2} - 6 x + 10 y + 2)

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} (2 y^{2}) - \frac{\partial}{\partial x} (6 x) + \frac{\partial}{\partial x} (10 y) + \frac{\partial}{\partial x} (2)

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

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

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

\frac{\partial}{\partial x} (6 x) = 6

\frac{\partial}{\partial x} (10 y) = 0

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

= 2 x + 2 y + 0 - 6 + 0 + 0

Simplify

= 2 x + 2 y - 6

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

\frac{( x ^{2} + 1 )}{( x - 1 ) ^{2}}

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 y)

\int \frac{x}{x ^{2} + y ^{2}} d y

f (x) = 9 e^{x}, at x = 7

What is (\partial)/(\partial x)(x^2+2xy+2y^2-6x+10y+2) ?
The answer to (\partial)/(\partial x)(x^2+2xy+2y^2-6x+10y+2) is 2x+2y-6