What is (\partial)/(\partial x)(ln(((2x-1))/(x-1))) ?

The answer to (\partial)/(\partial x)(ln(((2x-1))/(x-1))) is -1/((2x-1)(x-1))

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(\partial)/(\partial x)(ln(((2x-1))/(x-1)))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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 \frac{1}{x} - \frac{6}{x ^{2} + 1} d x

f (x) = sin (cos (x^{2}))

n = 1 \sum \infty 3 n^{5}

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

\frac{\partial}{\partial z} (3 x sin (y - z))

What is (\partial)/(\partial x)(ln(((2x-1))/(x-1))) ?
The answer to (\partial)/(\partial x)(ln(((2x-1))/(x-1))) is -1/((2x-1)(x-1))