What is (\partial)/(\partial x)(xy+xz-2yz) ?

The answer to (\partial)/(\partial x)(xy+xz-2yz) is y+z

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(\partial)/(\partial x)(xy+xz-2yz)

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

y + z

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{\partial}{\partial x} (2 yz) = 0

= y + z - 0

Simplify

= y + z

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