Then you're supposed to know derivatives of simple functions like sines and cosines.

你应该知道一些简单函数的导数,比如正弦函数和余弦函数

耶鲁公开课 - 基础物理课程节选

I'm using the fact that when you take a cosine and change the angle inside the cosine, it doesn't care. whereas, if you go to the sine and change the angle inside the sine, it becomes minus sine.

我用了一个结论,当你使用余弦函数时,改变角度的正负,函数值不变,而对于正弦函数,改变角度的符号,则函数值也会变号

耶鲁公开课 - 基础物理课程节选

For example, this is x=t, x=t^, you're going to have x=sin t and cos t and log t.

例如,这是x=t,x=t^,你还会遇到正弦,余弦,对数函数

耶鲁公开课 - 基础物理课程节选