What is (\partial)/(\partial x)(x^2-4xy+y^2+6y+3) ?

The answer to (\partial)/(\partial x)(x^2-4xy+y^2+6y+3) is 2x-4y

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(\partial)/(\partial x)(x^2-4xy+y^2+6y+3)

\frac{\partial}{\partial x} (x^{2} - 4 x y + y^{2} + 6 y + 3)

2 x - 4 y

Solution steps

\frac{\partial}{\partial x} (x^{2} - 4 x y + y^{2} + 6 y + 3)

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} (4 x y) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (6 y) + \frac{\partial}{\partial x} (3)

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

\frac{\partial}{\partial x} (4 x y) = 4 y

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

\frac{\partial}{\partial x} (6 y) = 0

\frac{\partial}{\partial x} (3) = 0

= 2 x - 4 y + 0 + 0 + 0

Simplify

= 2 x - 4 y

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What is (\partial)/(\partial x)(x^2-4xy+y^2+6y+3) ?
The answer to (\partial)/(\partial x)(x^2-4xy+y^2+6y+3) is 2x-4y