Question

r(s) = sq. root 2s+1
r'(s) = ?

Answer 1

\[r(s)=\sqrt{2x+1}\]Equivalently, we can write
\[r(s)=(2x+1)^{\frac{1}{2}}\]This second form is more useful to us.
\[r'(s)=\frac{1}{2}(2)(2x+1)^{-{\frac{1}{2}}}\]
That 1/2 is coming from the power, and that 2 comes from the chain rule.
Cleaning it up a little and replacing the rational power with a square root, we get
\[r'(s)=\frac{1}{\sqrt{2x+1}}\]