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

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

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

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

\frac{1}{y + z}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{y + z}

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