en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln((1-x/(1+x)))

Solution

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

Solution

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of (1+5x)^{6/x}

x \to 0 lim ((1 + 5 x)^{\frac{6}{x}})

integral of 5cos(x^2)

\int 5 cos (x^{2}) d x

slope ofintercept (4,-1),(-1,-4)slope intercept

(4, - 1), (- 1, - 4)

inverse oflaplace 1/(s^2+s^1+s^1+1)inverse laplace

\frac{1}{s ^{2} + s ^{1} + s ^{1} + 1}

integral of 1/(usqrt(5-u^2))

\int \frac{1}{u 5 - u ^{2}} d u

Frequently Asked Questions (FAQ)

What is the derivative of ln((1-x/(1+x))) ?
The derivative of ln((1-x/(1+x))) is -2/((-x+1)(x+1))
What is the first derivative of ln((1-x/(1+x))) ?
The first derivative of ln((1-x/(1+x))) is -2/((-x+1)(x+1))