What is the derivative of ln((5x+1/(5x-1))) ?

The derivative of ln((5x+1/(5x-1))) is -(10)/((5x+1)(5x-1))

What is the first derivative of ln((5x+1/(5x-1))) ?

The first derivative of ln((5x+1/(5x-1))) is -(10)/((5x+1)(5x-1))

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\frac{d}{d x} (ln (\frac{5 x + 1}{5 x - 1}))

- \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

Solution steps

\frac{d}{d x} (ln (\frac{5 x + 1}{5 x - 1}))

Apply the chain rule:

\frac{1}{\frac{5 x + 1}{5 x - 1}} \frac{d}{d x} (\frac{5 x + 1}{5 x - 1})

= \frac{1}{\frac{5 x + 1}{5 x - 1}} \frac{d}{d x} (\frac{5 x + 1}{5 x - 1})

\frac{d}{d x} (\frac{5 x + 1}{5 x - 1}) = - \frac{10}{( 5 x - 1 ) ^{2}}

= \frac{1}{\frac{5 x + 1}{5 x - 1}} (- \frac{10}{( 5 x - 1 ) ^{2}})

Simplify

\frac{1}{\frac{5 x + 1}{5 x - 1}} (- \frac{10}{( 5 x - 1 ) ^{2}}) : - \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

= - \frac{10}{( 5 x + 1 ) ( 5 x - 1 )}

What is the derivative of ln((5x+1/(5x-1))) ?
The derivative of ln((5x+1/(5x-1))) is -(10)/((5x+1)(5x-1))
What is the first derivative of ln((5x+1/(5x-1))) ?
The first derivative of ln((5x+1/(5x-1))) is -(10)/((5x+1)(5x-1))