随着【suízhe】

随着 opens a phrase about something that is changing, and the main clause describes a second change that follows from it or moves with it. It is neutral to formal, and common in writing about society, technology and growing up.

The main clause usually carries a word of change: 越来越, 也, 逐渐, 不断, 变得.

随着 + noun + 的 + verb

The phrase after 随着 is usually built as a noun: X 的 + a change verb like 发展, 提高, 增加, 变化, 推移. A full clause sounds unfinished.

• × 随着经济发展很快 → 随着经济的快速发展
• × 随着时间过 → 随着时间的推移

Not "with" a person

English "with" in "I went with my friend" is 跟 or 和. 随着 only tracks one change against another.

• × 我随着朋友去了公园 → 我跟朋友去了公园