en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (ln(x)^{-2})

Solution

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

Solution

- \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 )}

Popular Examples

integral of 2x^{1/3}

\int 2 x^{\frac{1}{3}} d x

limit as x approaches infinity of cos(x)

x \to \infty lim (cos (x))

y^{''}+12y^'+36y=e^{-5x}(x^2-2x+3)

y^{^{''}} + 12 y^{^{'}} + 36 y = e^{- 5 x} (x^{2} - 2 x + 3)

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

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

sum from n=0 to infinity of 1/((2n)!)

n = 0 \sum \infty \frac{1}{( 2 n ) !}

Frequently Asked Questions (FAQ)

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))