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

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

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

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

y + z

Solution steps

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

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

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

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

= y + z + 0

Simplify

= y + z

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