What is (\partial)/(\partial y)(x^2-y^3-x^2y+y) ?

The answer to (\partial)/(\partial y)(x^2-y^3-x^2y+y) is 1-x^2-3y^2

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(\partial)/(\partial y)(x^2-y^3-x^2y+y)

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

1 - x^{2} - 3 y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{2}) - \frac{\partial}{\partial y} (y^{3}) - \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (y)

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

\frac{\partial}{\partial y} (y^{3}) = 3 y^{2}

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

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

= 0 - 3 y^{2} - x^{2} + 1

Simplify

= 1 - x^{2} - 3 y^{2}

\int_{1}^{R} \frac{ln ( 4 x )}{x ^{2}} d x

\int \frac{e}{π} d x

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

\frac{e ^{x}}{x ^{n}}

I n (x^{2})

What is (\partial)/(\partial y)(x^2-y^3-x^2y+y) ?
The answer to (\partial)/(\partial y)(x^2-y^3-x^2y+y) is 1-x^2-3y^2