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

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

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

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

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

- \frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{- 1}) = - \frac{1}{x ^{2}}

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

Simplify

\frac{1}{x ^{- 1}} (- \frac{1}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

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