Differentiation 微分 之二 以公式法求函數的微分.

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1 Differentiation 微分 之二 以公式法求函數的微分

2 基本函數的微分公式 Type 函數形式 Function f(x) Derivative df(x)/dx c=constant 常數 c
Power of x xa axa-1 Trigonometric 三角函數 sin x cos x tan x sec2 x Logarithmic 對數函數 ln x 1/x Exponential 指數函數 ex

3 Example 4.9 y=x5 f(x) = x -1/2 f(x) = x 0.3 Power of x f(x)=xa
df(x)/dx=axa-1 y=x5 f(x) = x -1/2 f(x) = x 0.3

4 Exercises differentiate by rule 由公式求微分
23. y=x3 24. x 4/5 25. x1/3 26. 1/x3

5 Differentiation of Combinations of functions 組合函數的微分法則
Type 函數形式 Rule 法則 Multiple of a function函數的倍數 Sum of functions 函數相加 Product rule 乘法律 Quotient rule 除法律 Chain rule 連鎖律 Inverse rule 倒數律

6 Example 4.11 Linear Combination of Function 函數的線性組合 (函數相加的微分)

7 Exercises differentiate by rule 由公式求微分

8 Exercises differentiate by rule 由公式求微分(應用題)

9 Product Rule 乘法律 (函數相乘的微分)

10 Example 4.12

11 Exercises differentiate by rule 由公式求微分

12 Exercises differentiate by rule 由公式求微分

13 Exercises differentiate by rule 由公式求微分

14 Example 4.13 Quotient Rule 除法律 (函數相除的微分)

15 Exercises differentiate by rule 由公式求微分

16 Exercises differentiate by rule 由公式求微分

17 Exercises differentiate by rule 由公式求微分

18 Exercises differentiate by rule 由公式求微分

19 待續 …