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

The derivative of (ln(x)^{-2}) is -2/(xln^3(x))

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

The first derivative of (ln(x)^{-2}) is -2/(xln^3(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{2}{x ln ^{3} ( x )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

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

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

What is the derivative of (ln(x)^{-2}) ?
The derivative of (ln(x)^{-2}) is -2/(xln^3(x))
What is the first derivative of (ln(x)^{-2}) ?
The first derivative of (ln(x)^{-2}) is -2/(xln^3(x))