What is (\partial)/(\partial x)(x(7-x-y)) ?

The answer to (\partial)/(\partial x)(x(7-x-y)) is -2x-y+7

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(\partial)/(\partial x)(x(7-x-y))

\frac{\partial}{\partial x} (x (7 - x - y))

- 2 x - y + 7

Solution steps

\frac{\partial}{\partial x} (x (7 - x - y))

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = 7 - x - y

= \frac{\partial}{\partial x} (x) (7 - x - y) + \frac{\partial}{\partial x} (7 - x - y) x

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

\frac{\partial}{\partial x} (7 - x - y) = - 1

= 1 \cdot (7 - x - y) + (- 1) x

Simplify

1 \cdot (7 - x - y) + (- 1) x : - 2 x - y + 7

= - 2 x - y + 7

x \to 0 lim (cot (7 x))

\int 9 tan (9 x) d x

x \to 5 lim (4 x)

\int (3 x + 2 y) d x

\frac{d}{d x} (- x ln (x))

What is (\partial)/(\partial x)(x(7-x-y)) ?
The answer to (\partial)/(\partial x)(x(7-x-y)) is -2x-y+7