Need help on 2 homework problems

Question

Hey, Need some help with two homework problems, thanks!

Find dr/ds where t is a constant. Show all work. r²+2s sqrt(t) = r*t

Determine if the statement is true or false.

If f is differentiable, then d/dx f(sqrt(x)) = f'(x)/(2 * sqrt(x))

Answer 1

2r dr/ds + 2√t = t dr/ds

dr/ds = -2t/(2r-t)

True, by the Chain Rule

Leibnitz notation for the chain rule : dy/dx = dy/du * du/dx which is easy to remember

or f'(x) = f'(u(x)) * u'(x)

In this case u(x)=√x.