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 )}

\frac{d}{d t} (3 t^{2} + 2 t + 1)

\frac{x ^{2}}{16}

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

b (1 - sin (x))

cot (x^{2} sin^{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))