What is the derivative of x/(x^{-4)} ?

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

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

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

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derivative of

\frac{x}{x ^{- 4}}

5 x^{4}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{- 4}})

Simplify

\frac{x}{x ^{- 4}} : x^{5}

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