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

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

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

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

2 x^{2} y - x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 x^{2} y - x + 0

Simplify

= 2 x^{2} y - x

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