Question

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

Answer 1

`= 35/2 * (1)/((4x-5)(3x+5 ))`

Explanation:

`d/dx ( ln sqrt((4x-5)/(3x+5)))`

`= d/dx ( 1/2 ln ((4x-5)/(3x+5)))`

`= 1/2 d/dx ( ln (4x-5) - ln(3x+5 ))`

`= 1/2 ( 4/(4x-5) - 3/(3x+5 ))`

`= 1/2 ( (12x + 20 -12 x+15)/((4x-5)(3x+5 )))`

`= 35/2 * (1)/((4x-5)(3x+5 ))`