## Calculus (3rd Edition)

$$U_r =(\frac{-1}{r^2}-\frac{t}{r})e^{-rt},\quad U_t= -e^{-rt}.$$
Recall the product rule: $(uv)'=u'v+uv'$ Recall that $(e^x)'=e^x$ Since $U=e^{-rt}/r=r^{-1}e^{-rt}$, then by using the product rule, we have $$U_r=-r^{-2}e^{-rt}+r^{-1}e^{-rt}(-t)=(\frac{-1}{r^2}-\frac{t}{r})e^{-rt},\\ U_t= r^{-1}e^{-rt}(-r)=-e^{-rt}.$$