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}

\frac{d}{d u} (tan (u))

\int tan^{2} (3 x) d x

\frac{d}{d x} (sin (x^{2 x}))

x \to 5 lim (\frac{∣ x - 5 ∣}{5 - x})

\frac{d}{d x} ((x + 5)^{3})

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