What is the derivative of ln((4x+3)/(3x-5)) ?

The derivative of ln((4x+3)/(3x-5)) is -(29)/((4x+3)(3x-5))

What is the first derivative of ln((4x+3)/(3x-5)) ?

The first derivative of ln((4x+3)/(3x-5)) is -(29)/((4x+3)(3x-5))

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derivative of

ln (\frac{4 x + 3}{3 x - 5})

- \frac{29}{( 4 x + 3 ) ( 3 x - 5 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 x + 3}{3 x - 5}))

Apply the chain rule:

\frac{1}{\frac{4 x + 3}{3 x - 5}} \frac{d}{d x} (\frac{4 x + 3}{3 x - 5})

= \frac{1}{\frac{4 x + 3}{3 x - 5}} \frac{d}{d x} (\frac{4 x + 3}{3 x - 5})

\frac{d}{d x} (\frac{4 x + 3}{3 x - 5}) = - \frac{29}{( 3 x - 5 ) ^{2}}

= \frac{1}{\frac{4 x + 3}{3 x - 5}} (- \frac{29}{( 3 x - 5 ) ^{2}})

Simplify

\frac{1}{\frac{4 x + 3}{3 x - 5}} (- \frac{29}{( 3 x - 5 ) ^{2}}) : - \frac{29}{( 4 x + 3 ) ( 3 x - 5 )}

= - \frac{29}{( 4 x + 3 ) ( 3 x - 5 )}

\int_{0}^{3} ∣ 2 x - 1 ∣ d x

(x^{2} + 1) \frac{d y}{d x} = x y

\int \frac{x ^{2}}{1 + 2 x ^{2}} d x

\int_{2}^{\infty} - 5 x^{- 2} d x

\frac{d}{d x} (5 x e^{4 x})

What is the derivative of ln((4x+3)/(3x-5)) ?
The derivative of ln((4x+3)/(3x-5)) is -(29)/((4x+3)(3x-5))
What is the first derivative of ln((4x+3)/(3x-5)) ?
The first derivative of ln((4x+3)/(3x-5)) is -(29)/((4x+3)(3x-5))