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

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

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

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

x + y

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial z} (x y) = 0

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

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

= 0 + y + x

Simplify

= x + y

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\frac{d}{d x} (\frac{3}{5 x ^{\frac{2}{5}}})

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