Im revising for an exam i have next week, and cannot for my life understand the solutions to this previous exam question:

http://i.imgur.com/hLGMwIp.jpg

Is this essentially the same question as:

z = f(x,y) , g = g(s,t), y = h(s,t)

and then find dz/ds and dz/dt ?

the solutions look like the employ implicit differentiation, but i am not sure. typically I am confused from the second line,

HOw is du/dr * dr/dt = -c * df/dr ?

My train of thought is dr/dt = -c

du/dr is another way of saying df/dr, and using that same deduction we get the second half of that equation

But then i am COMPLETELY lost on the third line

Any help would be appreciated.

Please explain to me, like I am an idiot though..

thank MHF, you're always a huge help