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证明和解释基本倒数规则。

基本导数法则告诉我们如何对常数函数、常数乘以函数,以及函数加/减进行求导。
常数法则start fraction, d, divided by, d, x, end fraction, k, equals, 0
常数乘法法则start fraction, d, divided by, d, x, end fraction, open bracket, k, dot, f, left parenthesis, x, right parenthesis, close bracket, equals, k, dot, start fraction, d, divided by, d, x, end fraction, f, left parenthesis, x, right parenthesis
加法法则start fraction, d, divided by, d, x, end fraction, open bracket, f, left parenthesis, x, right parenthesis, plus, g, left parenthesis, x, right parenthesis, close bracket, equals, start fraction, d, divided by, d, x, end fraction, f, left parenthesis, x, right parenthesis, plus, start fraction, d, divided by, d, x, end fraction, g, left parenthesis, x, right parenthesis
减法法则start fraction, d, divided by, d, x, end fraction, open bracket, f, left parenthesis, x, right parenthesis, minus, g, left parenthesis, x, right parenthesis, close bracket, equals, start fraction, d, divided by, d, x, end fraction, f, left parenthesis, x, right parenthesis, minus, start fraction, d, divided by, d, x, end fraction, g, left parenthesis, x, right parenthesis
AP微积分课程不要求我们证明这一事实,但我们相信只要可以证明,我们就可以从中学习。一般来说,能够用某种证明去证实学到的定理是对的,总是好的。

让我们先来看一下为什么常数法则成立。

可汗学院视频播放器
The derivative of a constant is 0查看视频字幕

现在让我们来证明常数乘法和加/减法法则。

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Basic differentiation rules查看视频字幕

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