Why is the derivative of a vector also a vector?

为什么矢量的导数还是一个矢量呢

耶鲁公开课 - 基础物理课程节选

Even though we started with a single vector, which is the position vector, we're now finding out that its derivative has to be a vector and the derivative of the derivative is also a vector.

即使我们从单个矢量出发,即位移矢量,我们现在也能得出它的导数是矢量,而且导数的导数也是一个矢量

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You can take a derivative of the derivative and you can get the acceleration vector, will be d^2r over dt^2, and you can also write it as dv over dt.

你可以对导数再求一次导,你就可以得到加速度矢量,也就是 d^2 r / dt^2,你也可以写成 dv / dt

耶鲁公开课 - 基础物理课程节选

take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.

对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r

耶鲁公开课 - 基础物理课程节选