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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (x + y) (- 1 \cdot z^{- 1 - 1})

Simplify

(x + y) (- 1 \cdot z^{- 1 - 1}) : - \frac{x + y}{z ^{2}}

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

ln (1 - e^{- x})

\frac{d}{d x} (4 x^{2} + 3 x - 7)

\int \frac{( x ^{3} )}{25 - x ^{2}} d x

n = 2 \sum \infty \frac{1}{n n}

x \to - \frac{4}{5} - lim (5 x + 4)

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