What is (\partial)/(\partial y)(x^4-2x^2y) ?

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

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(\partial)/(\partial y)(x^4-2x^2y)

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

- 2 x^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{4}) = 0

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

= 0 - 2 x^{2}

Simplify

= - 2 x^{2}

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