derivative of [ln(x)]^2 ;x=e^2

Question

wikiemol · Answer

e^2 is just a constant so the whole derivative would be 0.

hartnn · Answer

you need to use chain rule, know what it is ?

anonymous · Answer

U gotta use the property of natural logs as well as the chain rule.
so u get:
2(ln(x))*1/x

for e^2 its the rule of e, which says that e^x is equal to e^x, so e^2 = e^2

anonymous · Answer

The chain rule would be the derivative 2[ln(x)]^1 times (1/x),right?

hartnn · Answer

that is correct,
now just plug in x=e^2

anonymous · Answer

oh u had to plug in? in that case, ignore the second part of my answer.

anonymous · Answer

2ln(e^2)*(1/e^2) would simplify to 2e/e^2 to 2/e?

hartnn · Answer

ln e=1
 so just 
2/e^2

hartnn · Answer

sorry, 4/e^2

anonymous · Answer

...?

anonymous · Answer

so dont the ln  and e cancel, leaving behind an e?

anonymous · Answer

sorry, the ln and e^2 cancel...right?

anonymous · Answer

I just don't understand this canceling part~

anonymous · Answer

it should be 4/e

anonymous · Answer

No, hartnn's answer is right, and I have the answers, I just dont know how to get to it~

anonymous · Answer

2 * 1/e^2 * 2e

anonymous · Answer

how did ln(e^2) become 2e?

anonymous · Answer

i am using the chain rule

anonymous · Answer

I used it and came out with 2*ln(e^2)*(1/e^2)
but I dont know how to go from there

anonymous · Answer

anyone?

anonymous · Answer

u didnt take the derivate of e^2 yet

anonymous · Answer

U just substitute it right in, right...?

anonymous · Answer

substitute?

anonymous · Answer

yeah, x=e^2, where i plugged it in when I couldn't go any farther with the x.

anonymous · Answer

so what's ln(e^2) simplified?

anonymous · Answer

1/e^2 * 2e

hartnn · Answer

use the property $\large \ln a^b=b\ln a$
so, $\ln e^2 = 2\ln e$
and ln e = 1

hartnn · Answer

$\ln e^2=2$

anonymous · Answer

no, not talking about the deriavtive of ln(e^2), Nageer ,simplified form~

hartnn · Answer

(2 ln e^2)/e^2= (2*2)/e^2 = 4/e^2

anonymous · Answer

OHHH I get it now, hartnn... but why wouldn't it be e? cos ln(e^2) is the same as ln(e)(e), right? OH, you can't take the log of one and not the other... oops :D got it

hartnn · Answer

sorry for the delayed reply...

anonymous · Answer

itz ok, u were offline for a little~ :)

anonymous · Answer

well, thanx!!! I got it~! well then, hasta luego!

hartnn · Answer

welcome ^_^