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

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

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

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

2 x + y + 6

Solution steps

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

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

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

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

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

= 2 x + y + 6 - 0

Simplify

= 2 x + y + 6

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\frac{3}{8 x ^{\frac{5}{2}}}

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