I am trying to show that the hazard function h(t)=-d/dt(ln(R(t))) is constant if and only if the variable has an exponential distribution where R(t) is the reliability 1-F(t) of a random variable with cdf F. I am not totally sure where to start in order to prove this in either direction.

Is it right to simplify to h(t)=F'(t)/(1-F(t)) and plug in?