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

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

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

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

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

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

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

Simplify

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

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

(- 2, 5.5), (0, 5.5)

\int \frac{5 x ^{2} + x - 34}{( x + 1 ) ^{2} ( x - 4 )} d x

\frac{x}{2}

\frac{d}{d x} (\frac{2 x + 7}{2 x})

- (- x^{3} + y^{3}) d x + x y^{2} d y = 0

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