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