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

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

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

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

\frac{3}{z}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 x) = 3

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

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

Simplify

\frac{1}{z} (3 + 0) : \frac{3}{z}

= \frac{3}{z}

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