Answer
The solution is
$$R_t(0,1)=1.$$
Work Step by Step
First, find the derivative:
$$R_t=(t e^{s/t})'_t=(t)'_te^{s/t}+t(e^{s/t})'_t=e^{s/t}+te^{s/t}(s/t)'_t=e^{s/t}+te^{s/t}\left(-\frac{s}{t^2}\right)=e^{s/t}-\frac{s}{t}e^{s/t}=e^{s/t}\left(1-\frac{s}{t}\right).$$
Now calculate by direct substitution $s=0$ and $t=1$:
$$R_t(0,1)=e^{0/1}\left(1-\frac{0}{1}\right)=1\cdot1=1.$$
