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

The answer to (\partial)/(\partial x)((x+y)/(z-2y)) is 1/(z-2y)

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

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

\frac{1}{z - 2 y}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{z - 2 y}

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What is (\partial)/(\partial x)((x+y)/(z-2y)) ?
The answer to (\partial)/(\partial x)((x+y)/(z-2y)) is 1/(z-2y)