What is the derivative of x^{-1} ?

The derivative of x^{-1} is -1/(x^2)

What is the first derivative of x^{-1} ?

The first derivative of x^{-1} is -1/(x^2)

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derivative of

x^{- 1}

- \frac{1}{x ^{2}}

Solution steps

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

Apply the Power Rule:

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

= - 1 \cdot x^{- 1 - 1}

Simplify

- 1 \cdot x^{- 1 - 1} : - \frac{1}{x ^{2}}

= - \frac{1}{x ^{2}}

\int \frac{1 - u}{1 + u} d u

x \to 0 lim (2 sin (x) - 1)

\int (\frac{ln ( x )}{x ^{2}}) d x

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

\int_{- 1}^{2} \frac{x ^{3}}{3} d x

What is the derivative of x^{-1} ?
The derivative of x^{-1} is -1/(x^2)
What is the first derivative of x^{-1} ?
The first derivative of x^{-1} is -1/(x^2)