What is (\partial}{\partial x}(\frac{8x+5y)/z) ?

The answer to (\partial}{\partial x}(\frac{8x+5y)/z) is 8/z

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(\partial}{\partial x}(\frac{8x+5y)/z)

\frac{\partial}{\partial x} (\frac{8 x + 5 y}{z})

\frac{8}{z}

Solution steps

\frac{\partial}{\partial x} (\frac{8 x + 5 y}{z})

Treat

y, z

as constants

Take the constant out:

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

= \frac{1}{z} \frac{\partial}{\partial x} (8 x + 5 y)

Apply the Sum/Difference Rule:

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

= \frac{1}{z} (\frac{\partial}{\partial x} (8 x) + \frac{\partial}{\partial x} (5 y))

\frac{\partial}{\partial x} (8 x) = 8

\frac{\partial}{\partial x} (5 y) = 0

= \frac{1}{z} (8 + 0)

Simplify

\frac{1}{z} (8 + 0) : \frac{8}{z}

= \frac{8}{z}

What is (\partial}{\partial x}(\frac{8x+5y)/z) ?
The answer to (\partial}{\partial x}(\frac{8x+5y)/z) is 8/z