What is the derivative of 1/(z^4) ?

The derivative of 1/(z^4) is -4/(z^5)

What is the first derivative of 1/(z^4) ?

The first derivative of 1/(z^4) is -4/(z^5)

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derivative of

\frac{1}{z ^{4}}

- \frac{4}{z ^{5}}

Solution steps

\frac{d}{d z} (\frac{1}{z ^{4}})

Apply exponent rule:

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

= \frac{d}{d z} (z^{- 4})

Apply the Power Rule:

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

= - 4 z^{- 4 - 1}

Simplify

- 4 z^{- 4 - 1} : - \frac{4}{z ^{5}}

= - \frac{4}{z ^{5}}

What is the derivative of 1/(z^4) ?
The derivative of 1/(z^4) is -4/(z^5)
What is the first derivative of 1/(z^4) ?
The first derivative of 1/(z^4) is -4/(z^5)