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

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

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

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

\frac{- x - y}{z ^{2}}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial z} (\frac{x}{z}) = - \frac{x}{z ^{2}}

\frac{\partial}{\partial z} (\frac{y}{z}) = - \frac{y}{z ^{2}}

= - \frac{x}{z ^{2}} - \frac{y}{z ^{2}}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- x - y}{z ^{2}}

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