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1·Why do we like partial derivatives?

为什么我们偏爱偏微分呢？

2·We are trying to understand partial derivatives.

我们还要试图理解偏导数。

3·It has only partial derivatives for each variable.

它只有关于每个变量的偏导数。

4·Suppose and have continuous partial derivatives on.

设，在上有连续的偏导数。

5·So, we have to figure out what we mean by partial derivatives again.

因此，我们应该重新理解偏导数的含义。

6·That means it involves the first partial derivatives of whatever you put into it.

这意味着，不管放什么进去，都会包括一阶偏导。

7·So, critical points, remember, are the points where all the partial derivatives are zero.

临界点是，偏导数都为零的点。

8·What we would start doing immediately is taking the partial derivatives. What is f sub x?

我们首先要做的事是,求偏导数，fx是多少？

9·And we have learned how to package partial derivatives into a vector, the gradient vector.

我们也知道了，如何将各个偏导组合成一个梯度向量。

10·And a partial differential equation is some relation between its partial derivatives. Let me see.

而一个偏微分方程就是，函数各个偏导之间的联系，看看。