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

Simplify

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

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

\int cos^{4} (7 x + 6) d x

\int \frac{1}{( 4 x - x ^{2} )} d x

\int_{0}^{1} (5 e^{x} - 5 x e^{x^{2}}) d x

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

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