1. The first derivative of the function shows where it is increasing or decreasing.
函数的一阶导数显示函数在哪些地方递增或递减。

2. To find the maximum point, we set the first derivative equal to zero.
为了找到最大值点，我们将一阶导数设为零。

3. The first derivative helps in analyzing the slope of the curve.
一阶导数有助于分析曲线的斜率。

A: How do you calculate the first derivative of this function?
A：你如何计算这个函数的一阶导数？

B: You differentiate it with respect to x.
B：对x求导就可以。

1) 函数的变化率

2) 曲线的斜率

3) 微积分中的基本工具

1. 函数的第一阶导数，用于表示函数的瞬时变化率或斜率

e.g. The first derivative of y = x^2 is 2x.
y = x^2 的一阶导数是 2x。

2. 用于判断函数的递增、递减或极值

e.g. Set the first derivative to zero to find critical points.
将一阶导数设为零以找到关键点。

noun

1. The first derivative of a function represents its instantaneous rate of change or slope at a given point.

Synonym: differential, rate of change