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

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

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(\partial)/(\partial z)(x/z)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

g (x) = ln (x e^{- 7 x})

\frac{\partial}{\partial y} (x^{2} y^{\frac{1}{3}})

\int \frac{u}{u ^{2} + 1} d u

x \to 0 lim (\frac{ln ( \frac{1 + x}{1 - x} ) - 2 x}{x - sin ( x )})

\int x x^{4} + 1 d x

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