What is (\partial)/(\partial x)(2xy(9-x-y)) ?

The answer to (\partial)/(\partial x)(2xy(9-x-y)) is 2y(-2x-y+9)

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(\partial)/(\partial x)(2xy(9-x-y))

\frac{\partial}{\partial x} (2 x y (9 - x - y))

2 y (- 2 x - y + 9)

Solution steps

\frac{\partial}{\partial x} (2 x y (9 - x - y))

Treat

y

as a constant

Take the constant out:

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

= 2 y \frac{\partial}{\partial x} (x (9 - x - y))

Apply the Product Rule:

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

f = x, g = 9 - x - y

= 2 y (\frac{\partial}{\partial x} (x) (9 - x - y) + \frac{\partial}{\partial x} (9 - x - y) x)

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

\frac{\partial}{\partial x} (9 - x - y) = - 1

= 2 y (1 \cdot (9 - x - y) + (- 1) x)

Simplify

2 y (1 \cdot (9 - x - y) + (- 1) x) : 2 y (- 2 x - y + 9)

= 2 y (- 2 x - y + 9)

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\frac{\partial}{\partial x} ((5 x + 4 y) e^{y})

What is (\partial)/(\partial x)(2xy(9-x-y)) ?
The answer to (\partial)/(\partial x)(2xy(9-x-y)) is 2y(-2x-y+9)