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

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

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

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

y - 2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4) = 0

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 0 - 2 x + y - 0

Simplify

= y - 2 x

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