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

看了一下二阶导数，也就是二阶条件。

Most great things in life are second derivatives of things.

生活中最伟大事物都是事物二阶导数。

Familiar example comes from calculus, the derivative.

们熟悉例子来自微积分 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 偏导数将是平坦。

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

在让们尝试使用幂法则找到更多导数。

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

为了找到最大值，希望二阶导数为负。

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

们将导数设为 0。

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

这是薄透镜透镜方程，它是导数 从射线照相几何形状。

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

同理，你可以取导数 找到加速度速度。

That one corresponds to the derivative of five X squared.

这个对应于5x²导数。

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

所以对这个对象进行了区分，这是一阶导数，将它设置为 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.

所以这个方向斜率，即关于 m 偏导数， 将是平坦。

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

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，如果要对该表达式求关于 m 偏导数。

So its partial derivative with respect to m is 0.

所以它对m偏导数为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，该导数必须满足什么条件？

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

但即使这只是们需要偏导数之一，它也完成了超过 50% 工作。

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

例如，们可以采取权力基地 与导数一起使用，反向应用。