If f(x) = ln(ln(1-x)), then f'(x) =

a) -1/ln(1-x)

b) 1/[(1-x)ln(1-x)]

c) 1/[(1-x)^2]

d) -1/[(1-x)ln(1-x)]

e) -1/[ln(1-x)^2]

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- Dec 26th 2007, 11:10 AMDINOCALC09derivative involving "ln"
If f(x) = ln(ln(1-x)), then f'(x) =

a) -1/ln(1-x)

b) 1/[(1-x)ln(1-x)]

c) 1/[(1-x)^2]

d) -1/[(1-x)ln(1-x)]

e) -1/[ln(1-x)^2] - Dec 26th 2007, 11:24 AMcolby2152
- Dec 26th 2007, 11:38 AMDINOCALC09
how does the double ln work [ln(ln(...]

- Dec 26th 2007, 11:49 AMcolby2152
- Dec 26th 2007, 11:51 AMTKHunny
All 'ln's work the same. It's just an application of the chain rule.

[f(g(h(x)))]' = f'(g(h(x)))*g'(h(x))*h'(x)

If f, g, and h are all the same, it just looks funny, it doesn't work any differently. - Dec 26th 2007, 11:54 AMbobak
?

you use the chain rule.

- Dec 26th 2007, 11:59 AMJhevon

Just a matter of applying the chain rule as others said. and of course, we assume 1/(anything) is defined and what not... - Dec 26th 2007, 12:23 PMIsomorphism
Ya others already said it, but if you are new to this,solve any such problem like this :

When you see ln (>something here<), at first step dont worry about >something here< just write 1/>something here< on paper. Now look at that >somethin here< it could be another function, say sin(>more something<), again forget what ever is inside parentheses just write derivative of sin (that is cos....) Keep on proceeding until you run out of functions.

__Example:__

say you are asked to__differentiate__

Yuck! Ugly function but don't worry...

Start Identifying functions from the >outermost< parts.

**What I do?**

***I tell myself, hey looks like some Y^4 ,so I write down: . Now let's fill "............"

***Now I see what's inside, hey looks like some (This is not the old Y, I am using Y as a variable!). I say to myself, I know it's derivative, it's , so I write down .

***Proceeding like this I notice next up is sin Y and its derivative is cos Y. So now I can happily write

Hope you get the idea :D

I know it looks complicated but it is just a matter of practice. So can you complete my answer ??

Hope you do well :) - Dec 26th 2007, 12:49 PMcolby2152
Good explanation of the chain rule guys! I always liked using the word "junk" when teaching the chain rule. Junk can contain a carrot, and you would have to take the derivative of carrot and multiply that by junk.

- Dec 26th 2007, 01:22 PMIsomorphism
- Dec 26th 2007, 01:55 PMKrizalid