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 e^{s i n (x)} \cdot cos (x) d x

\int \frac{x - 11}{x ^{2} + 3 x - 4} d x

n = 0 \sum \infty \frac{4 ^{n}}{n !}

x \to \infty lim (1. 1^{x})

x \to 1 lim (x^{4} - 3 x^{2} + 6)

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))