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

The answer to (\partial)/(\partial y)((2-x)(y-2)(3-x-y)) is (2-x)(5-x-2y)

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

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

(2 - x) (5 - x - 2 y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = y - 2, g = 3 - x - y

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

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

\frac{\partial}{\partial y} (3 - x - y) = - 1

= (2 - x) (1 \cdot (3 - x - y) + (- 1) (y - 2))

Simplify

(2 - x) (1 \cdot (3 - x - y) + (- 1) (y - 2)) : (2 - x) (5 - x - 2 y)

= (2 - x) (5 - x - 2 y)

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What is (\partial)/(\partial y)((2-x)(y-2)(3-x-y)) ?
The answer to (\partial)/(\partial y)((2-x)(y-2)(3-x-y)) is (2-x)(5-x-2y)