I'm having trouble getting from u_s to u_(ss). Could someone elaborate on that part a great deal. I'm pretty sure I get the rest. It's just the partial differentiation algebra which confuses me.

Even for the u_s part: I'm pretty sure f_x is a partial derivative but is x_s also a apartial derivative (to use the first summand of u_s as an example)?

Any input would be greatly appreciated!

Thanks in advance!