文档介绍：该【2023年微积分知识点总结 】是由【知识徜徉土豆】上传分享，文档一共【7】页，该文档可以免费在线阅读，需要了解更多关于【2023年微积分知识点总结 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。A DERIVATIVE FUNCTION
The derivative function or simply the derivative is defined as
＝＝
Find the derivative function
Find ,
Find the average rate of change ,
Find the limit .
Geometric significance
Consider a general function y=f(x), a fixed point A(a,f(a)) and a variable point B(x,f(x)). The slope of chord AB=.
Now as BA, xa and the slope of chord ABslope of tangent at A.
So, is .
Thus, we can know the derivative at x=a is the slope of the tangent at x=a.
Rules
C(a constant)
0
The chain rule
If where then .
,
6. Inverse function, Parametric function and Implicit function
Inverse function:, ,
., ,
Parametric function:,
., ,→,
Implicit function: , .
, , t
High derivative
y=sinx ,
B APPLICATIONS OF DIFFERENTIAL CALCULUS
Monotonicity
If S is an interval of real numbers and f(x) is defined for all x in S, then：
f(x) is increasing on S for all x in S, and
f(x) is decreasing on S for all x in S.
Find the monotone interval
Find domain of the function,
Find , and x which make ,
Draw sign diagram, find the monotone interval.
Maxima/Minima, Horizontal inflection, Stationary point
C INTEGRAL
The idea of definite integral
We define the unique number between all lower and upper sums as and call it “the definite integral of from a to b”,
., where .
We note that as , and
We write .
If for all x on [a,b] then is the shaded area.
Properties of definite integrals
, c is any constant
, where
（f(x) odd）,(f(x)even)
If on then
If on then
The average value of a function on an interval [a,b]
The infinite integral
If , then
Formulas:,
,,,
(),
U Substitution
substitution u=g(x)
Integration by Parts