In other words, it’s the derivative of mass-times-velocity with respect to time.

换句话说，它是质量乘以速度对时间的。

That one corresponds to the derivative of five X squared.

这个对应5x²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。

Break it down into smaller, manageable goals such as understanding limits, derivatives, and integrals.

将分解为更小的、可管理的目标，例如理解极限、和积分。

So we'd call velocity the derivative of position, and acceleration the derivative of velocity.

所以我们速度为位置的， 加速度是速度的。

In other words, it's the derivative of mass-times-velocity with respect to time.

换句话说，它是一个 （质量乘以速度）相对时间。

And the partial derivative of this with respect to b, set that equal to 0.

并将 b 的偏设为 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。

And the partial derivative of our squared error with respect to b is going to be equal to 0.

并且我们的平方误差 b 的偏将等 0。

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

提醒一下，偏，就像取正则一样。

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

b 的偏将是平坦的。

Familiar example comes from calculus, the derivative.

我们熟悉的例子来自微积分 。

We can actually try to guess the derivative of sin(x) just by looking at its graph.

我们可以猜测 sin(x) 的 只看图表。

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， 即我们之为的知识， 与直觉知识相对。

So, to find your velocity, we’ll need to find the derivative of your position.

所以，要找到你的速度， 我们需要找到你的位置的。

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 m 的偏。

In other words, its change -- and therefore its derivative -- must be negative.

换句话说，改变它...... 等等 它的… … 它一定是负。

His method of " fluxions" or infinitesimals, while controversial at the time, set the groundwork for our modern concept of limits and derivatives.

他的“流”或无穷小方法虽然在当时颇受争议，但却为我们现代的极限和概念奠定了基础。

So its partial derivative with respect to m is 0.

所以它对m的偏为0。

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

同理，你可以取 找到加速度的速度。