So maybe you can tell me,

也许你可以告诉我
what should I do to check that this is a conservative force?

我应该怎么做来验证这是个保守力
Yes. I will repeat what he said;

对的我来重复一下他说的
that's the correct answer.

这是正确的回答
I must take the x component of this, take the y partial derivative,

x 分量对 y 求偏导数
the y component of this, take an x partial derivatives.

y 分量对 x 求偏导数
You guys should do that.

你们应该动手算一算
When you take the derivative of something like 1 / r^3,

当你做像 1 / r^3 这样的导数运算时
you should first take the r derivative of 1 / r^3,

你应该首先求 1 / r^3 对 r 的导数
and then take the x derivative of r or the y derivative.

然后求 r 对 x 的导数或对 y 的导数
Using the Chain Rule of calculus,

使用微积分的链式法则
you'll find the two agree.

你会发现两个导数相等