What is (\partial)/(\partial x)((3x-3z)/(2y+3z)) ?

The answer to (\partial)/(\partial x)((3x-3z)/(2y+3z)) is 3/(2y+3z)

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(\partial)/(\partial x)((3x-3z)/(2y+3z))

\frac{\partial}{\partial x} (\frac{3 x - 3 z}{2 y + 3 z})

\frac{3}{2 y + 3 z}

Solution steps

\frac{\partial}{\partial x} (\frac{3 x - 3 z}{2 y + 3 z})

Treat

z, y

as constants

Take the constant out:

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

= \frac{1}{2 y + 3 z} \frac{\partial}{\partial x} (3 x - 3 z)

Apply the Sum/Difference Rule:

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

= \frac{1}{2 y + 3 z} (\frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (3 z))

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

\frac{\partial}{\partial x} (3 z) = 0

= \frac{1}{2 y + 3 z} (3 - 0)

Simplify

\frac{1}{2 y + 3 z} (3 - 0) : \frac{3}{2 y + 3 z}

= \frac{3}{2 y + 3 z}

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What is (\partial)/(\partial x)((3x-3z)/(2y+3z)) ?
The answer to (\partial)/(\partial x)((3x-3z)/(2y+3z)) is 3/(2y+3z)