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

The derivative of ln((x+1/(sqrt(x-1)))) is (x-3)/(2(x+1)(x-1))

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

The first derivative of ln((x+1/(sqrt(x-1)))) is (x-3)/(2(x+1)(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 - 1}))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

2 cos (2 t)

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

\int \frac{1}{6 x lo g _{7} ( x )} d x

\int 3 x^{2} y + e^{y} d x

What is the derivative of ln((x+1/(sqrt(x-1)))) ?
The derivative of ln((x+1/(sqrt(x-1)))) is (x-3)/(2(x+1)(x-1))
What is the first derivative of ln((x+1/(sqrt(x-1)))) ?
The first derivative of ln((x+1/(sqrt(x-1)))) is (x-3)/(2(x+1)(x-1))