m116ex01a - 1 N ote. XIV-1. I am posting the solutions to...

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1 N ote. XIV-1. I am posting the solutions to three sample problems by the requests of your fellow classmates. The problems are solved using the tech- nique of Logarithmic Differentiation. Hope you can see the similarity among the problems, and learn the true spirit of this technique. N Important: Note. Q uestion XIV-1. ( Sample ) Find the derivative of the function f ( x ) = 3 x + 5(2 x - 3) 4 . W ork XIV-1. The derivative will be computed using the technique of Log- arithmic Differentiation as shown below. f ( x ) = 3 x + 5(2 x - 3) 4 (1) ln( f ( x )) = law of logarithms #1 z }| { ln ( 3 x + 5(2 x - 3) 4 ) = ln ( 3 x + 5 ) + ln ( (2 x - 3) 4 ) (2) = law of logarithms #3 z }| { 1 2 ln(3 x + 5) + law of logarithms #3 z }| { 4ln(2 x - 3) (3) [ln( f ( x ))] 0 = 1 2 ln(3 x + 5) 0 + [4ln(2 x - 3)] 0 (4) f 0 ( x ) f ( x ) = 1 2 · (3 x + 5) 0 3 x + 5 + 4 · (2 x - 3) 0 2 x - 3 (5) f 0 ( x ) f ( x ) = 1 2 · 3 + 0 3 x + 5 + 4 · 2 - 0 2 x - 3 (6) f 0 ( x ) f ( x ) = 3 2(3 x + 5) + 8 2 x - 3 (7) f
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m116ex01a - 1 N ote. XIV-1. I am posting the solutions to...

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