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+1)/x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of e^{x/(y^2)}

\int e^{\frac{x}{y ^{2}}} d x

integral of (tan(ln(3x+2)))/(3x+2)

\int \frac{tan ( ln ( 3 x + 2 ) )}{3 x + 2} d x

integral from 0 to 4 of ((t^2)/3+2t)

\int_{0}^{4} (\frac{t ^{2}}{3} + 2 t) d t

integral of 1/(9-8x)

\int \frac{1}{9 - 8 x} d x

integral of (xe^{3x})/((1+3x)^2)

\int \frac{x e ^{3 x}}{( 1 + 3 x ) ^{2}} d x

Frequently Asked Questions (FAQ)

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