Question

Use Logarithmic Differentiation to find dy/dx given that y=(((2x+4)^2)sqrroot(2x-2))/(x+6)

Answer 1

take the log and simplify your %^&* off
you get

\[\ln(\text{stuff})=2\ln(2x+4) +\frac{1}{2}\ln(2x-2)+\ln(x+6)\]

Answer 2

then take the derivative which is now easy you get
\[\frac{4}{2x+4}+\frac{1}{2x-2}-\frac{1}{x+6}\]

Answer 3

typo on first line last term should be
\[-\ln(x+6)\]

Answer 4

now multiply by original function and you are done

Answer 5

sweet thanks man caught one thing u didnt do though 4/2x+4 = 2/x+2 but thank you so much :D:D:

Answer 6

maybe typos here but you get the idea. take the log, simplify using properties of the log, then take the derivative and then multiply by the original function. don't forget the chain rule!

Answer 7

eww... chain rule... gah i hate differentiation