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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

n = 1 \sum \infty \frac{7}{( n + 1 ) !}

\frac{d}{d x} (x^{2} 6 x - 7)

ln (5 x^{2} + 7 y^{2})

f (x) = 1 + 5 e^{x}, at x = 1

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

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