What is (\partial)/(\partial x)(324x^2-324xy+81y^2) ?

The answer to (\partial)/(\partial x)(324x^2-324xy+81y^2) is 648x-324y

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(\partial)/(\partial x)(324x^2-324xy+81y^2)

\frac{\partial}{\partial x} (324 x^{2} - 324 x y + 81 y^{2})

648 x - 324 y

Solution steps

\frac{\partial}{\partial x} (324 x^{2} - 324 x y + 81 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (324 x^{2}) - \frac{\partial}{\partial x} (324 x y) + \frac{\partial}{\partial x} (81 y^{2})

\frac{\partial}{\partial x} (324 x^{2}) = 648 x

\frac{\partial}{\partial x} (324 x y) = 324 y

\frac{\partial}{\partial x} (81 y^{2}) = 0

= 648 x - 324 y + 0

Simplify

= 648 x - 324 y

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What is (\partial)/(\partial x)(324x^2-324xy+81y^2) ?
The answer to (\partial)/(\partial x)(324x^2-324xy+81y^2) is 648x-324y