What is (\partial)/(\partial x)(-5xy(9-x-y)) ?

The answer to (\partial)/(\partial x)(-5xy(9-x-y)) is -5y(-2x-y+9)

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(\partial)/(\partial x)(-5xy(9-x-y))

\frac{\partial}{\partial x} (- 5 x y (9 - x - y))

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

Solution steps

\frac{\partial}{\partial x} (- 5 x y (9 - x - y))

Treat

y

as a constant

Take the constant out:

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

= - 5 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

= - 5 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

= - 5 y (1 \cdot (9 - x - y) + (- 1) x)

Simplify

- 5 y (1 \cdot (9 - x - y) + (- 1) x) : - 5 y (- 2 x - y + 9)

= - 5 y (- 2 x - y + 9)

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What is (\partial)/(\partial x)(-5xy(9-x-y)) ?
The answer to (\partial)/(\partial x)(-5xy(9-x-y)) is -5y(-2x-y+9)