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

我看了一下二导数，也就是二件。

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导数。

Familiar example comes from calculus, the derivative.

我们熟悉的例子来自微积分 导数。

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

提醒一下，偏导数，就像取正则导数一样。

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

关于 b 的偏导数将是平坦的。

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则找到更多的导数。

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

了找到最大值，我希望二导数。

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

我们将发现的导数设 0。

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

这是薄透镜透镜方程，它是导数 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，你可以取导数 找到加速度的速度。

That one corresponds to the derivative of five X squared.

这个对应于5x²的导数。

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，这是我的一导数，我将它设置 0。

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

最多，这个导数必定是什么？

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 的偏导数， 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导数时，数学家们想出了捷径。

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 的偏导数。

So its partial derivative with respect to m is 0.

所以它对m的偏导数0。

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

那么，了将其转变一件，该导数必须满足什么件？

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导数之一，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，我们可以采取权力基地 与导数一起使用，反向应用。