What is (\partial)/(\partial z)(xz+xyz) ?

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

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(\partial)/(\partial z)(xz+xyz)

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

x + x y

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= x + x y

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