What is the derivative of ln(x^{-2}) ?

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

What is the first derivative of ln(x^{-2}) ?

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

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

- \frac{2}{x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

= \frac{1}{x ^{- 2}} (- \frac{2}{x ^{3}})

Simplify

\frac{1}{x ^{- 2}} (- \frac{2}{x ^{3}}) : - \frac{2}{x}

= - \frac{2}{x}

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(ln (y))^{6} \frac{d y}{d x} = x^{6} y, y (1) = e^{2}

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