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))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\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}} \cdot \frac{1}{x ^{2}}

Simplify

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

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

100 (1 + A e^{- t})^{- 1}

\int x^{5} 7 + x^{6} d x

\int t^{2} cos (2 t) d t

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

f (x) = x \cdot 1 - x^{2}, [0, 1]

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))