m116ex01a

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online