Question

use logarithm differentiation to find dy/dx for the following


y=(8x + 1)^3 e^x/ sqrt(4x^2 + 1)

Answer 1

take ln of both sides
\[lny = \ln[(8x+1)^3]+lne^x-\ln[\sqrt{4x^2+1}]\]

Answer 2

\[lny = 3\ln[8x+1]+xlne-1/2\ln[4x^2+1]\]

Answer 3

\[lny = 3\ln[8x+1]+x-1/2\ln[4x^2+1]\]

Answer 4

lne = 1 so the lne goes away in that last one

Answer 5

\[1/y*dy/dx = 24/(8x+1)+1-4/(4x^2+1)\]

Answer 6

\[1/y*dy/dx = 24/[4*(2x+1)]+1-4/[(2x+1)(2x-1)]\]

Answer 7

etc

multiply by y and replace y with the original equation