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

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

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(\partial)/(\partial z)(y/z)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{x}{1 + x}

\frac{d}{d x} ((A x^{2} + B x) e^{- x})

\frac{d}{d t} (\frac{2 t}{t ^{2} + 2})

arccot (3 x)

n = 1 \sum \infty \frac{n !}{1 4 ^{n}}

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