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

derivative of

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}} \cdot \frac{4}{( x + 2 ) ^{2}}

Simplify

\frac{1}{\frac{x - 2}{x + 2}} \cdot \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))