What is the derivative of ln(sqrt((1+x/(1-x)))) ?

The derivative of ln(sqrt((1+x/(1-x)))) is 1/((-x+1)(x+1))

What is the first derivative of ln(sqrt((1+x/(1-x)))) ?

The first derivative of ln(sqrt((1+x/(1-x)))) is 1/((-x+1)(x+1))

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{1 + x}{1 - x}))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of ln(sqrt((1+x/(1-x)))) ?
The derivative of ln(sqrt((1+x/(1-x)))) is 1/((-x+1)(x+1))
What is the first derivative of ln(sqrt((1+x/(1-x)))) ?
The first derivative of ln(sqrt((1+x/(1-x)))) is 1/((-x+1)(x+1))