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

The derivative of (1+1/x /(1-1/x)) is -2/((x-1)^2)

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

The first derivative of (1+1/x /(1-1/x)) is -2/((x-1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = e^{3 x} \cdot e^{2 y}

x \to 3 lim (\frac{x ^{2} + 3}{x - 1})

\int x^{2} x^{3} + 31 d x

y = \frac{3}{x}, y = \frac{x}{12}, 1 \leq x \leq 6

x \to 0 lim (- 1 + \frac{1}{x})

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