What is (\partial)/(\partial x)((4x-4z)/(3y+4z)) ?

The answer to (\partial)/(\partial x)((4x-4z)/(3y+4z)) is 4/(3y+4z)

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(\partial)/(\partial x)((4x-4z)/(3y+4z))

\frac{\partial}{\partial x} (\frac{4 x - 4 z}{3 y + 4 z})

\frac{4}{3 y + 4 z}

Solution steps

\frac{\partial}{\partial x} (\frac{4 x - 4 z}{3 y + 4 z})

Treat

z, y

as constants

Take the constant out:

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

= \frac{1}{3 y + 4 z} \frac{\partial}{\partial x} (4 x - 4 z)

Apply the Sum/Difference Rule:

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

= \frac{1}{3 y + 4 z} (\frac{\partial}{\partial x} (4 x) - \frac{\partial}{\partial x} (4 z))

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (4 z) = 0

= \frac{1}{3 y + 4 z} (4 - 0)

Simplify

\frac{1}{3 y + 4 z} (4 - 0) : \frac{4}{3 y + 4 z}

= \frac{4}{3 y + 4 z}

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What is (\partial)/(\partial x)((4x-4z)/(3y+4z)) ?
The answer to (\partial)/(\partial x)((4x-4z)/(3y+4z)) is 4/(3y+4z)