What is the derivative of ln((2x+3)/(3x-4)) ?

The derivative of ln((2x+3)/(3x-4)) is -(17)/((2x+3)(3x-4))

What is the first derivative of ln((2x+3)/(3x-4)) ?

The first derivative of ln((2x+3)/(3x-4)) is -(17)/((2x+3)(3x-4))

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derivative of

ln (\frac{2 x + 3}{3 x - 4})

- \frac{17}{( 2 x + 3 ) ( 3 x - 4 )}

Solution steps

\frac{d}{d x} (ln (\frac{2 x + 3}{3 x - 4}))

Apply the chain rule:

\frac{1}{\frac{2 x + 3}{3 x - 4}} \frac{d}{d x} (\frac{2 x + 3}{3 x - 4})

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

\frac{d}{d x} (\frac{2 x + 3}{3 x - 4}) = - \frac{17}{( 3 x - 4 ) ^{2}}

= \frac{1}{\frac{2 x + 3}{3 x - 4}} (- \frac{17}{( 3 x - 4 ) ^{2}})

Simplify

\frac{1}{\frac{2 x + 3}{3 x - 4}} (- \frac{17}{( 3 x - 4 ) ^{2}}) : - \frac{17}{( 2 x + 3 ) ( 3 x - 4 )}

= - \frac{17}{( 2 x + 3 ) ( 3 x - 4 )}

\int \frac{7}{35 sin ( x ) - 12 cos ( x )} d x

\int_{0}^{t} e^{- x^{2}} d x

n = 0 \sum \infty (- 3 x)^{n}

x \to 0 lim (1 - cos^{2} (x))

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What is the derivative of ln((2x+3)/(3x-4)) ?
The derivative of ln((2x+3)/(3x-4)) is -(17)/((2x+3)(3x-4))
What is the first derivative of ln((2x+3)/(3x-4)) ?
The first derivative of ln((2x+3)/(3x-4)) is -(17)/((2x+3)(3x-4))