During any given day's practice, you'll eventually gonna hit a wall where you stop making progress whether it's learning derivatives in calculus or kickflips in skateboarding.

你最终会在某一天的学习中——无论是学习微积分的导数还是滑板的踢翻——碰到一堵墙，阻隔你的进步。

And then you take the second derivative, de-development over time, and that's evolution.

然后你取时间的二阶导数，即去发展，这就是进化。

Yeah, but so it came from Hinton having, introduce the concept of define your objective function, figure out how to take the derivatives so that you can adjust the connections so that they make progress towards your goal.

是的，但这一切都源于辛顿提出了定义目标函数的，出如何计算导数，便你可调整连接，使其朝着你的目标前进。

So on screen right now, there's kinda lot of symbols, so take a moment to make sure it's clear what they all are, because now we are gonna compute the relevant derivatives.

所现在屏幕上有很多符号，点时间确保你清楚它们都是什么，因为我们现在要计算相关的导数。

Just like with a normal derivative, we can write the variation of E times t as E times the variation of t plus t times the variation of E.

就像普通导数一样，我们可 E t 的变化写为 E t 的变化加上 t E 的变化。

But there are certain other elements which the given factors determine so completely that we can treat these derivatives as being themselves given.

但是还有某些其他因素完全由给定因素决定，至于我们可这些导数视为它们本身是给定的。

Years earlier, I'd noticed that when I got sad or anxious, often the second derivative of those feelings made them doubly upsetting.

几年前， 我注意到当我感到悲伤或焦虑时，这些情绪的二阶导数往往会令它们变得更加令人不安。

You said it's a little second derivative, but I'm not too sure, so I wanted to double check your thoughts on NRG.

你说这有点二次导数的味道，但我不是太确定， 所想再确认一下你对NRG的看法。

Based on what you already know about acceleration, you can already guess that angular acceleration is the derivative of angular velocity.

根据你对加速度的了解，你已经可猜到角加速度是角速度的导数。

It can, therefore, at best define one sort of knowledge, the sort we call derivative, as opposed to intuitive knowledge.

因此，它最多只能定义一种知识， 即我们称之为导数的知识， 与直觉知识相对。

So, anybody who's done calculus knows that the first derivative is good, the second derivative is not so good?

所， 任何学过微积分的人都知道， 一阶导数是好的，二阶导数就没那么好了？

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

所我对这个对象进行了区分，这是我的一阶导数，我它设置为 0。

The partial derivative of that with respect to b is just going to be the coefficient.

关于b的偏导数就是系数。

Minus the derivative of the potential is just the force.

减去势的导数就是力。

Or are we into the third derivative?

或者我们已经进入到了三级导数？

It's too much second derivative, so to speak.

可这么说，这是过于复杂的二阶导数。

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导数。

But, you know, when you have metabolism, you know, anatomy and physiology, and you take the first derivative with respect to time, De-metabolism over time, and that's development.

但是，你知道，当你有了代谢、解剖学和生理学，然后你对时间求一阶导数，即随时间变化的代谢过程，那就是发育。

Meaning, at those points, the equations aren't changing at all -- so the derivative at these turning points is also going to be exactly zero.

意思是，在那些点上，方程式根本没有改变——所这些转折点处的导数也恰好为零。

It says for a given time and for a given state, which is going to have XYZ coordinates, just what's the derivative of that state.

它表示在给定的时间和给定的状态下，该状态的XYZ坐标导数是什么。