What is (\partial)/(\partial x)((2+x)(y-x)) ?

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

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(\partial)/(\partial x)((2+x)(y-x))

\frac{\partial}{\partial x} ((2 + x) (y - x))

- 2 x + y - 2

Solution steps

\frac{\partial}{\partial x} ((2 + x) (y - x))

Treat

y

as a constant

Apply the Product Rule:

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

f = 2 + x, g = y - x

= \frac{\partial}{\partial x} (2 + x) (y - x) + \frac{\partial}{\partial x} (y - x) (2 + x)

\frac{\partial}{\partial x} (2 + x) = 1

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

= 1 \cdot (y - x) + (- 1) (2 + x)

Simplify

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

= - 2 x + y - 2

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