What is (\partial}{\partial x}(\frac{x+y+z)/3) ?

The answer to (\partial}{\partial x}(\frac{x+y+z)/3) is 1/3

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(\partial}{\partial x}(\frac{x+y+z)/3)

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

\frac{1}{3}

Solution steps

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

Treat

y, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{\partial}{\partial x} (x + y + z)

Apply the Sum/Difference Rule:

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

= \frac{1}{3} (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (z))

\frac{\partial}{\partial x} (x) = 1

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

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

= \frac{1}{3} (1 + 0 + 0)

Simplify

= \frac{1}{3}

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What is (\partial}{\partial x}(\frac{x+y+z)/3) ?
The answer to (\partial}{\partial x}(\frac{x+y+z)/3) is 1/3