随着 and 从而 — changing together, and leading to

规则 随着 + a PROCESS in motion，and the second clause moves with it: 随着年龄的增长，他变得成熟了。
What follows 随着 is usually a noun phrase with 的 (的增长, 的发展), not a full clause.
从而 = and thereby — attaching a logical consequence: 他改进了方法，从而提高了效率。
从而 only opens a second clause and takes no subject of its own.