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

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

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

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

y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 - 0 + y

Simplify

= y

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

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