What is (\partial)/(\partial x)(4xy(-12-x-y)) ?

The answer to (\partial)/(\partial x)(4xy(-12-x-y)) is 4y(-2x-y-12)

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(\partial)/(\partial x)(4xy(-12-x-y))

\frac{\partial}{\partial x} (4 x y (- 12 - x - y))

4 y (- 2 x - y - 12)

Solution steps

\frac{\partial}{\partial x} (4 x y (- 12 - x - y))

Treat

y

as a constant

Take the constant out:

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

= 4 y \frac{\partial}{\partial x} (x (- 12 - x - y))

Apply the Product Rule:

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

f = x, g = - 12 - x - y

= 4 y (\frac{\partial}{\partial x} (x) (- 12 - x - y) + \frac{\partial}{\partial x} (- 12 - x - y) x)

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

\frac{\partial}{\partial x} (- 12 - x - y) = - 1

= 4 y (1 \cdot (- 12 - x - y) + (- 1) x)

Simplify

4 y (1 \cdot (- 12 - x - y) + (- 1) x) : 4 y (- 2 x - y - 12)

= 4 y (- 2 x - y - 12)

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What is (\partial)/(\partial x)(4xy(-12-x-y)) ?
The answer to (\partial)/(\partial x)(4xy(-12-x-y)) is 4y(-2x-y-12)