What is the derivative of ln((3x+4/(3x-4))) ?

The derivative of ln((3x+4/(3x-4))) is -(24)/((3x+4)(3x-4))

What is the first derivative of ln((3x+4/(3x-4))) ?

The first derivative of ln((3x+4/(3x-4))) is -(24)/((3x+4)(3x-4))

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\frac{d}{d x} (ln (\frac{3 x + 4}{3 x - 4}))

- \frac{24}{( 3 x + 4 ) ( 3 x - 4 )}

Solution steps

\frac{d}{d x} (ln (\frac{3 x + 4}{3 x - 4}))

Apply the chain rule:

\frac{1}{\frac{3 x + 4}{3 x - 4}} \frac{d}{d x} (\frac{3 x + 4}{3 x - 4})

= \frac{1}{\frac{3 x + 4}{3 x - 4}} \frac{d}{d x} (\frac{3 x + 4}{3 x - 4})

\frac{d}{d x} (\frac{3 x + 4}{3 x - 4}) = - \frac{24}{( 3 x - 4 ) ^{2}}

= \frac{1}{\frac{3 x + 4}{3 x - 4}} (- \frac{24}{( 3 x - 4 ) ^{2}})

Simplify

\frac{1}{\frac{3 x + 4}{3 x - 4}} (- \frac{24}{( 3 x - 4 ) ^{2}}) : - \frac{24}{( 3 x + 4 ) ( 3 x - 4 )}

= - \frac{24}{( 3 x + 4 ) ( 3 x - 4 )}

What is the derivative of ln((3x+4/(3x-4))) ?
The derivative of ln((3x+4/(3x-4))) is -(24)/((3x+4)(3x-4))
What is the first derivative of ln((3x+4/(3x-4))) ?
The first derivative of ln((3x+4/(3x-4))) is -(24)/((3x+4)(3x-4))