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

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

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

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

- 2 y + 2

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (4 x^{2}) = 0

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

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

= 0 - 2 y + 2

Simplify

= - 2 y + 2

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