What is the derivative of ln((5x+3/(5x-3))) ?

The derivative of ln((5x+3/(5x-3))) is -(30)/((5x+3)(5x-3))

What is the first derivative of ln((5x+3/(5x-3))) ?

The first derivative of ln((5x+3/(5x-3))) is -(30)/((5x+3)(5x-3))

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\frac{d}{d x} (ln (\frac{5 x + 3}{5 x - 3}))

- \frac{30}{( 5 x + 3 ) ( 5 x - 3 )}

Solution steps

\frac{d}{d x} (ln (\frac{5 x + 3}{5 x - 3}))

Apply the chain rule:

\frac{1}{\frac{5 x + 3}{5 x - 3}} \frac{d}{d x} (\frac{5 x + 3}{5 x - 3})

= \frac{1}{\frac{5 x + 3}{5 x - 3}} \frac{d}{d x} (\frac{5 x + 3}{5 x - 3})

\frac{d}{d x} (\frac{5 x + 3}{5 x - 3}) = - \frac{30}{( 5 x - 3 ) ^{2}}

= \frac{1}{\frac{5 x + 3}{5 x - 3}} (- \frac{30}{( 5 x - 3 ) ^{2}})

Simplify

\frac{1}{\frac{5 x + 3}{5 x - 3}} (- \frac{30}{( 5 x - 3 ) ^{2}}) : - \frac{30}{( 5 x + 3 ) ( 5 x - 3 )}

= - \frac{30}{( 5 x + 3 ) ( 5 x - 3 )}

\int 2 cot (2 x) d x

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n = 0 \sum \infty \frac{3}{( n + 1 )}

\frac{x ^{3}}{2} + \frac{1}{6 x}

What is the derivative of ln((5x+3/(5x-3))) ?
The derivative of ln((5x+3/(5x-3))) is -(30)/((5x+3)(5x-3))
What is the first derivative of ln((5x+3/(5x-3))) ?
The first derivative of ln((5x+3/(5x-3))) is -(30)/((5x+3)(5x-3))