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

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

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

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

2 - x - 2 y

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = y, g = 2 - x - y

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

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

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

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

Simplify

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

= 2 - x - 2 y

\int x (x^{2} + 1) d x

x y^{^{'}} - y^{^{'}} - (x - 1) sin (x) + y = 0

\int_{0}^{1} (1 + x^{2}) e^{- x} d x

y = \frac{7}{3 - 4 x ^{4}}

(x + 1) y^{^{'}} + (2 x - 1) y = e^{- 2 x}

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