in a careful way to avoid upsetting people

This is a very delicate situation and it needs to be handled sensitively. 这是一个非常微妙的情况，需要谨慎处理。

in a way that shows you understand a character in a play, story, etc. or the feelings in a piece of music

The solo was played very sensitively by the viola player. 独奏的中提琴手对作品的处理细致敏锐。

It was beautifully written and sensitively directed. 作品写得漂亮，导演得细腻入微。

in a way that reacts quickly to small changes or easily records small changes

Muscles respond sensitively to minute amounts of this electric current. 肌肉对微量的这种电流（也）会做出灵敏的反应。

in a way that involves becoming upset or angry easily

Maybe I'm reacting too sensitively. 我可能反应得太过敏感了。