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

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

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

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

x - 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= x - 0 - 2 y

Simplify

= x - 2 y

\frac{d}{d x} (∣ x ∣^{2})

\int x e^{4 - x^{2}} d x

x \to \frac{π}{6} lim (\frac{sin ( x )}{x})

y^{^{''}} + 64 y = \frac{32}{3} cos (7 t)

3 - x^{2}, 7 - 5 x

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