What is the derivative of 1/(x^{-5}) ?

The derivative of 1/(x^{-5}) is 5x^4

What is the first derivative of 1/(x^{-5}) ?

The first derivative of 1/(x^{-5}) is 5x^4

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\frac{d}{d x} (\frac{1}{x ^{- 5}})

5 x^{4}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{- 5}})

Apply exponent rule:

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

= \frac{d}{d x} (x^{5})

Apply the Power Rule:

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

= 5 x^{5 - 1}

Simplify

= 5 x^{4}

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