What is (\partial)/(\partial z)(1/z) ?

The answer to (\partial)/(\partial z)(1/z) is -1/(z^2)

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(\partial)/(\partial z)(1/z)

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

- \frac{1}{z ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 1 \cdot z^{- 1 - 1}

Simplify

- 1 \cdot z^{- 1 - 1} : - \frac{1}{z ^{2}}

= - \frac{1}{z ^{2}}

\int \frac{w ^{2} + 16}{w ^{2} - 16} d w

\frac{1}{( s - 2 ) ( s - 4 )}

y^{^{'''}} - 12 y^{^{''}} + 52 y^{^{'}} - 96 y = 0

y = e^{x}, y = 7 e^{- x} + 6, x = 0

What is (\partial)/(\partial z)(1/z) ?
The answer to (\partial)/(\partial z)(1/z) is -1/(z^2)