What is (\partial)/(\partial x)(x(10-x-y)) ?

The answer to (\partial)/(\partial x)(x(10-x-y)) is -2x-y+10

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(\partial)/(\partial x)(x(10-x-y))

\frac{\partial}{\partial x} (x (10 - x - y))

- 2 x - y + 10

Solution steps

\frac{\partial}{\partial x} (x (10 - x - y))

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = 10 - x - y

= \frac{\partial}{\partial x} (x) (10 - x - y) + \frac{\partial}{\partial x} (10 - x - y) x

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

\frac{\partial}{\partial x} (10 - x - y) = - 1

= 1 \cdot (10 - x - y) + (- 1) x

Simplify

1 \cdot (10 - x - y) + (- 1) x : - 2 x - y + 10

= - 2 x - y + 10

What is (\partial)/(\partial x)(x(10-x-y)) ?
The answer to (\partial)/(\partial x)(x(10-x-y)) is -2x-y+10