What is the d/(dz)(1/(z^2)) ?

The d/(dz)(1/(z^2)) is -2/(z^3)

What is the first d/(dz)(1/(z^2)) ?

The first d/(dz)(1/(z^2)) is -2/(z^3)

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\frac{d}{d z} (\frac{1}{z ^{2}})

- \frac{2}{z ^{3}}

Solution steps

\frac{d}{d z} (\frac{1}{z ^{2}})

Apply exponent rule:

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

= \frac{d}{d z} (z^{- 2})

Apply the Power Rule:

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

= - 2 z^{- 2 - 1}

Simplify

- 2 z^{- 2 - 1} : - \frac{2}{z ^{3}}

= - \frac{2}{z ^{3}}

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