I take a look at the second derivative, which is the second order condition.

我看了一下二阶，也就是二阶条件。

Most great things in life are second derivatives of things.

生活中最伟大的事物都是事物的二阶。

Familiar example comes from calculus, the derivative.

我们熟悉的例子来自微积分 。

Just as a reminder, partial derivatives, it's just like taking a regular derivative.

提醒一下，偏，就像取正一样。

The partial derivative with respect to b is going to be flat.

关于 b 的偏将是平坦的。

Now let’s try to find a couple more derivatives using the power rule.

现在让我们尝试使用幂法到更多的。

To find a maximum I want the second derivative to be negative.

为了到最大值，我希望二阶为负。

We set the thing we found, the derivative, equal to 0.

我们将发现的设为 0。

This is the thin lens equation, which is derived from ray diagram geometry.

这是薄透镜透镜方程，它是 从射线照相的几何形状。

In the same way, you could take the derivative of your velocity and find your acceleration.

同理，你以取 到加速度的速度。

That one corresponds to the derivative of five X squared.

这个对应于5x²的。

So I differentiated this object, this is my first derivative and I set it equal to 0.

所以我对这个对象进行了区分，这是我的一阶，我将它设置为 0。

At the maximum, what must be true about this derivative?

最多，这个必定是什么？

So the slope in this direction, that's the partial derivative with respect to m, is going to be flat.

所以这个方向的斜率，即关于 m 的偏， 将是平坦的。

Now, when it comes to how you can express a derivative in writing, mathematicians have come up with shortcuts.

现在，当涉及到如何以书面形式表达时，学家们想出了捷径。

So if I were to take the partial derivative of this expression with respect to m.

因此，如果我要对该表达式求关于 m 的偏。

So its partial derivative with respect to m is 0.

所以它对m的偏为0。

So to turn this into a first order condition what must be true about this derivative?

那么，为了将其转变为一阶条件，该必须满足什么条件？

But even though it was just one of those partial derivatives we need, it's more than 50% of the work.

但即使这只是我们需要的偏之一，它也完成了超过 50% 的工作。

For instance, you can take the power rule that we used for derivatives, and run it backward.

例如，我们以采取权力基地 与一起使用，反向应用。