I can get the first derivative, but in all my math/physic classes, I've never encountered this method. And I can't keep things straight enough to get past the first derivative unless it's very simple (which it usually isn't). The problem I am working on can be seen here: http://tinyurl.com/j2unrtp. I have the answer key already but the result is painful, and the bits I did accomplish match up, but the answer starts grouping like terms instead of keeping them expanded and results in a lot of confusion on my part.
The length is $L = 1050mm = \sqrt(S_A^2+250^2)+\sqrt(S_A^2+(S_B-250)^2)$
I achieved the first derivative: $L'=0=(S_A*S_A')/\sqrt(S_A^2+250^2)+(S_A*S_A')\sqrt(/S_A^2+(S_B-250)^2)+[(S_B-250)*S_B']/\sqrt(S_A^2+(S_B-250)^2)$
I have started the second and have gotten as far as taken care of the first term: $S_A'^2/\sqrt(S_A^2+250^2)+(S_A*S_A')/\sqrt(S_A^2+250^2)+$... but that's it. The next term has $S_B$ as well as $S_A$ and its derivative.
I'm pulling my hair out trying to keep track of what is going on, and taking derivatives to boot. I've been in a number of physics classes and never encountered this notation, and I just ... can't understand too much at once. E.g. anything past a first derivative (and sometimes even just the first). Is there not a clearer way of doing this, or some other notation?