What is (\partial)/(\partial y)(y(-2x-y+1)) ?

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

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(\partial)/(\partial y)(y(-2x-y+1))

\frac{\partial}{\partial y} (y (- 2 x - y + 1))

- 2 y - 2 x + 1

Solution steps

\frac{\partial}{\partial y} (y (- 2 x - y + 1))

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = - 2 x - y + 1

= \frac{\partial}{\partial y} (y) (- 2 x - y + 1) + \frac{\partial}{\partial y} (- 2 x - y + 1) y

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

\frac{\partial}{\partial y} (- 2 x - y + 1) = - 1

= 1 \cdot (- 2 x - y + 1) + (- 1) y

Simplify

1 \cdot (- 2 x - y + 1) + (- 1) y : - 2 y - 2 x + 1

= - 2 y - 2 x + 1

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