live birth
「生産」 has another reading with different meanings.
production; manufacture
生産の痛みは想像以上だった。
The pain of childbirth was beyond imagination.
無事に生産を終えた。
The delivery went smoothly.
妹の生産に付き添うために病院へ急いだ。
I rushed to the hospital to be with my sister for her delivery.