What is (\partial)/(\partial x)(1000-4xy+xy^2) ?

The answer to (\partial)/(\partial x)(1000-4xy+xy^2) is y^2-4y

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(\partial)/(\partial x)(1000-4xy+xy^2)

\frac{\partial}{\partial x} (1000 - 4 x y + x y^{2})

y^{2} - 4 y

Solution steps

\frac{\partial}{\partial x} (1000 - 4 x y + x y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (1000) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (x y^{2})

\frac{\partial}{\partial x} (1000) = 0

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

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

= 0 - 4 y + y^{2}

Simplify

= y^{2} - 4 y

What is (\partial)/(\partial x)(1000-4xy+xy^2) ?
The answer to (\partial)/(\partial x)(1000-4xy+xy^2) is y^2-4y