What is the derivative of 1/(x^n) ?

The derivative of 1/(x^n) is -nx^{-n-1}

What is the first derivative of 1/(x^n) ?

The first derivative of 1/(x^n) is -nx^{-n-1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{x ^{n}}

- n x^{- n - 1}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{n}})

Apply exponent rule:

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

= \frac{d}{d x} (x^{- n})

Apply the Power Rule:

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

= - n x^{- n - 1}

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