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.
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