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 )}

\int sin (t) 2 t d t

\int \frac{sin ( 2 x )}{e ^{x}} d x

\frac{d}{d x} (\frac{4 e ^{x}}{2 e ^{x} + 1})

2 sin (2 t)

\frac{d y}{d x} y = \frac{x ^{3}}{3} - x

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))