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

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

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

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

- y (- 2 x - y + 12)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - 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

= - 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

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

Simplify

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

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

\frac{\partial}{\partial t} (ln (x + t^{2}))

\frac{d}{d x} (\frac{7 + 8 x - 4 x}{x})

\int \frac{484 - x ^{2}}{x} d x

a re a x^{3}, x + 6 = y, \frac{- x}{2} = y

\frac{\partial}{\partial y} (ln (x y))

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