国际课程提前学Alevel数学微积分7：相关变化率

今天的国际课程提前学，给大家带来的是：Alevel数学微积分7：相关变化率，请大家一起来学习吧！（后附视频解读哦~）

conceptual analysis

概念解析

One important use of the Chain Rule is to find the rates of change of two or more related variables that are changing with respect to time.

链式法则的一个重要应用是解决多个变量的相关变化率问题。

The chain rule makes it possible to differentiate with respect to a variable which does not feature in the original expression.

However, you might be more interested in finding  the rate of change of volume with time, t. To find this, you would use the chain rule:

通过链式法则，我们可以对不在原函数中出现的变量进行求导。以球体积的变化率为例，可以将体积V，半径r，还有时间t的变化关系统一到一起。

Example 1

一块石头掉到了池塘中，水里的波纹是个同心圆，半径增大的速度是8厘米每秒，当半径是25厘米时，面积的变化率是多少？

Example 2

空气被注入一个气球，球体积变大的速度是4.5立方英尺每分钟。求当半径是2英尺的时候，球半径的变化率。