How do I find the derivative of $ln \sqrt{\frac{4 x - 5}{3 x + 5}}$ $ln sqrt((4x-5)/(3x+5))$ ?

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Answer 1 · 2016-08-07T12:06:57

$= \frac{35}{2} \cdot \frac{1}{(4 x - 5) (3 x + 5)}$ $= 35/2 * (1)/((4x-5)(3x+5 ))$

$\frac{d}{d x} (ln \sqrt{\frac{4 x - 5}{3 x + 5}})$ $d/dx ( ln sqrt((4x-5)/(3x+5)))$

$= \frac{d}{d x} (\frac{1}{2} ln (\frac{4 x - 5}{3 x + 5}))$ $= d/dx ( 1/2 ln ((4x-5)/(3x+5)))$

$= \frac{1}{2} \frac{d}{d x} (ln (4 x - 5) - ln (3 x + 5))$ $= 1/2 d/dx ( ln (4x-5) - ln(3x+5 ))$

$= \frac{1}{2} (\frac{4}{4 x - 5} - \frac{3}{3 x + 5})$ $= 1/2 ( 4/(4x-5) - 3/(3x+5 ))$

$= \frac{1}{2} (\frac{12 x + 20 - 12 x + 15}{(4 x - 5) (3 x + 5)})$ $= 1/2 ( (12x + 20 -12 x+15)/((4x-5)(3x+5 )))$

$= \frac{35}{2} \cdot \frac{1}{(4 x - 5) (3 x + 5)}$ $= 35/2 * (1)/((4x-5)(3x+5 ))$

How do I find the derivative of ln√4x−53x+5ln sqrt((4x-5)/(3x+5))?