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 )}

\frac{d}{d u} (2 u)

x (x^{2} + 1)

f (x) = x^{2} - 1, x = - 1, x = 1

sec^{2} (7 x)

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

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))