Answer
$$ R'(s)= 2 s^{\ln s-1}\ln s.$$
Work Step by Step
Since $ R(s)=s^{\ln s}$, applying $\ln $ on both sides, we get
$$\ln R(s)=\ln s^{\ln s}=\ln s \ln s=(\ln s)^2$$
Hence the derivative, using the chain rule, is given by
$$ R'(s)/R(s)=2\ln s (\ln s)'=\frac{2\ln s}{s} .$$
Then, we have
$$ R'(s)=\frac{2\ln s}{s} R(s)=\frac{2\ln s}{s} s^{\ln s} =2 s^{\ln s-1}\ln s.$$
