I can move along x, I can move along y,

我可以沿着 x 轴移动也可以沿着 y 轴移动
I can move at some intermediate angle,

还可以沿中间的某个角度移动
we have to ask

你必须要问
what do you want me to do

当要求导时
when it comes time to take derivatives.

你想让我做什么
So, it turns out, and you will see it proven amply as we go along,

晚点你会看到大量详细的证明
that you just have to think about

你会发现原来只用考虑
derivatives on two principle directions

两个主要方向的导数
which I will choose to be x and y.

我把它们选为 x 方向和 y 方向
So, we're going to define one derivative,

我们来定义一个导数
which is defined as follows.

它是这样定义的
You start at the point (x, y),

起点是 (x, y)