this is the only way it can happen.

这是唯一的方法
In other words,

换句话说
we all agree that if you got a force from a potential by taking derivatives,

我们都知道通过对势函数求导得到一个力
it does the job.

是可以实现的
But I'm saying, every force whose integral is independent of path

但我要说对任意一个积分与路径无关的力
will always have as its ancestor a function U,

总能找到一个函数 U
and the x component of the force will be

力的 x 分量
the x derivative of the function

就是这个函数对 x 的偏导数
and the y will be the y derivative.

y 分量就是函数对 y 的偏导数
That's not obvious,

这不是显而易见的
but in other words it's clear it's sufficient

但它既是充分的
but it's also necessary.

也是必要的