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

The answer to (\partial)/(\partial y)(x^2y-x-xy^2+y) is x^2-2xy+1

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

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

x^{2} - 2 x y + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial y} (y) = 1

= x^{2} - 0 - 2 x y + 1

Simplify

= x^{2} - 2 x y + 1

\frac{d}{d x} (1 8^{x})

x \to 0 lim (cos (19 x))

\frac{\partial}{\partial x} (ln (x^{3} y + 2 z))

\int sin^{3} (3 x) cos (3 x) d x

x \to 0 lim (x^{2} tan (x))

What is (\partial)/(\partial y)(x^2y-x-xy^2+y) ?
The answer to (\partial)/(\partial y)(x^2y-x-xy^2+y) is x^2-2xy+1