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

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Answer 1 · 2016-08-07T12:06:57

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

#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 ))#