1·It has only partial derivatives for each variable.
它只有关于每个变量的偏导数。
2·That was this symbolic vector operator in which the components are the partial derivative operators.
这个是符号化的向量算子，其中它的分量是偏微分算子。
3·If you have a single variable then the partial, with respect to that variable, is the same thing as the usual derivative.
如果只有一个变量，要求关于这个变量的偏导，这和通常求导是一样的。
4·And just to tell you again that is a strange partial differential equation relating these two vector fields.
再说明一下，这是关于这两个向量场，多少有点奇怪的偏微分方程。
5·Expect one about a min/max problem, something about Lagrange multipliers, something about the chain rule and something about constrained partial derivatives.
有一个极值问题，也有关于拉格朗日乘数法的，链式法则也会有的,约束条件下偏导数当然不会漏掉。