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

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

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

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

2 x - 2 y

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = x - 2 y

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

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

\frac{\partial}{\partial x} (x - 2 y) = 1

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

Simplify

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

= 2 x - 2 y

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