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

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

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

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

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

Simplify

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

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

\int x^{10} ln (x) d x

\int_{4}^{9} \frac{1}{1 - x} d x

\int e^{x^{3} + 1} d x

(1 + x^{2}) y^{^{'}} - 2 x y = 0

x \to 10 lim (\frac{x ^{3}}{3})

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