What is (\partial}{\partial z}(\frac{xy)/z) ?

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

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(\partial}{\partial z}(\frac{xy)/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}}

\frac{\partial}{\partial x} (7 - x^{4} + 2 x^{2} - y^{2})

\frac{d y}{d x} + 5 y = e^{x} y^{- 2}

\frac{d}{d x} ((x^{2} - 2) sin (x) + 2 x cos (x))

x \to 2 lim (\frac{∣ x - 3 ∣}{x - 3})

\int tan^{3} (5 x) sec^{2} (5 x) d x

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