Using Log Theorem to Derive Terms in Calculus 2

[Chocolaty]

I'm taking cal 2 right now and i missed the part in cal 1 where he talked about "log theorem". Now this guy tells us that he's lazy when he corrects exams and if we don't use the log theorem to derive a term then he won't correct that term. I've looked on the net but couldn't find explanation or theorem.

Here's an example of a term where he used it.
cos[(3x-2)^4]

When i derive this term I use the generalized power rule:
[u(x)]^n => n*u^(n-1)*u'
cos[(3x-2)^4] => -sin[(3x-2)^4]*4(3x-2)^3*(3)
He came up with this answer:
-2(3x-2)^4*4(3x-2)^3*(3)

Can anybody explain to me how one uses the log theorem?

 

[d_leet]

I have never heard of that before, and I definitely don't see how it's possible to get what you're teacher got for that derivative. Your way seems correct, so maybe you should ask you're teacher what the "log theorem" is..

 

[Chocolaty]

ok.

Does anybody know what this term actually means?
ln( x y )
There's no plus or minus or whatever.

 

[d_leet]

ok.

Does anybody know what this term actually means?
ln( x y )
There's no plus or minus or whatever.

Is it maybe supposed to mean, ln( f(x,y) ) where f(x,y) is a function of the two variables x and y?

 

[0rthodontist]

Maybe he means logarithmic differentiation. That wouldn't work for the function you gave though.

 

[HallsofIvy]

ok.

Does anybody know what this term actually means?
ln( x y )
There's no plus or minus or whatever.

looks like log x+ log y to me!