Sensitivity analysis is done to undersrand the impact of inputs (potential x's) on the desired output. And root cause analysis is done to identify the potential root causes of faults. That is, what x's has caused y. Root cause is basically a problem solving tool however sensitivity analysis a mathematical tool to model best possible scenario for outputs and studying the impacts of inputs and rearranging them.
So basically in a way both these methods is used to understand the effects of inputs on outputs.
This is why both relates to each other.