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

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

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

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

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derivative of

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

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

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

Simplify

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

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

x \to 3 lim (\frac{sin ( x )}{x})

\int \frac{72}{1 - cos ( 9 x )} d x

\frac{d}{d x} (x^{2} - y)

\frac{( 4 + x )}{( x - 2 )}, at x = 8

\frac{4}{x}

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