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

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

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

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

z + y

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= z + 0 + y

Simplify

= z + y

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