What is the derivative of ln((x+2/(x-2))) ?

The derivative of ln((x+2/(x-2))) is -4/((x+2)(x-2))

What is the first derivative of ln((x+2/(x-2))) ?

The first derivative of ln((x+2/(x-2))) is -4/((x+2)(x-2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{4}{( x + 2 ) ( x - 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 2}{x - 2}) = - \frac{4}{( x - 2 ) ^{2}}

= \frac{1}{\frac{x + 2}{x - 2}} (- \frac{4}{( x - 2 ) ^{2}})

Simplify

\frac{1}{\frac{x + 2}{x - 2}} (- \frac{4}{( x - 2 ) ^{2}}) : - \frac{4}{( x + 2 ) ( x - 2 )}

= - \frac{4}{( x + 2 ) ( x - 2 )}

What is the derivative of ln((x+2/(x-2))) ?
The derivative of ln((x+2/(x-2))) is -4/((x+2)(x-2))
What is the first derivative of ln((x+2/(x-2))) ?
The first derivative of ln((x+2/(x-2))) is -4/((x+2)(x-2))