What is the derivative of ln((2x+3/(2x-3))) ?

The derivative of ln((2x+3/(2x-3))) is -(12)/((2x+3)(2x-3))

What is the first derivative of ln((2x+3/(2x-3))) ?

The first derivative of ln((2x+3/(2x-3))) is -(12)/((2x+3)(2x-3))

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\frac{d}{d x} (ln (\frac{2 x + 3}{2 x - 3}))

- \frac{12}{( 2 x + 3 ) ( 2 x - 3 )}

Solution steps

\frac{d}{d x} (ln (\frac{2 x + 3}{2 x - 3}))

Apply the chain rule:

\frac{1}{\frac{2 x + 3}{2 x - 3}} \frac{d}{d x} (\frac{2 x + 3}{2 x - 3})

= \frac{1}{\frac{2 x + 3}{2 x - 3}} \frac{d}{d x} (\frac{2 x + 3}{2 x - 3})

\frac{d}{d x} (\frac{2 x + 3}{2 x - 3}) = - \frac{12}{( 2 x - 3 ) ^{2}}

= \frac{1}{\frac{2 x + 3}{2 x - 3}} (- \frac{12}{( 2 x - 3 ) ^{2}})

Simplify

\frac{1}{\frac{2 x + 3}{2 x - 3}} (- \frac{12}{( 2 x - 3 ) ^{2}}) : - \frac{12}{( 2 x + 3 ) ( 2 x - 3 )}

= - \frac{12}{( 2 x + 3 ) ( 2 x - 3 )}

\frac{d}{d x} (e^{x^{3} + 5})

\int x^{- 4} d x

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

x^{2} y^{^{''}} - x y^{^{'}} + y = 2 x

\frac{d}{d x} (x + x + 3)

What is the derivative of ln((2x+3/(2x-3))) ?
The derivative of ln((2x+3/(2x-3))) is -(12)/((2x+3)(2x-3))
What is the first derivative of ln((2x+3/(2x-3))) ?
The first derivative of ln((2x+3/(2x-3))) is -(12)/((2x+3)(2x-3))