高數(shù)導(dǎo)數(shù)與微分課件

第三章導(dǎo)數(shù)與微分1、定義：一、導(dǎo)數(shù)的概念機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分其它形式：即機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分注意:2、導(dǎo)函數(shù)機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分2）右導(dǎo)數(shù):1）左導(dǎo)數(shù):3、單側(cè)導(dǎo)數(shù)機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分4、基本導(dǎo)數(shù)公式機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分5、按定義求導(dǎo)數(shù)步驟:例1、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例2、解：練習(xí)1、討論機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例3、解:練習(xí)2、設(shè)解:機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分6、導(dǎo)數(shù)的幾何意義切線方程為法線方程為機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例4、解：由導(dǎo)數(shù)的幾何意義,知所求切線斜率為故所求切線方程為法線方程為機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分7、可導(dǎo)與連續(xù)的關(guān)系:

可導(dǎo)必連續(xù)，但連續(xù)不一定可導(dǎo).機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例5、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分記作三階導(dǎo)數(shù):(二階和二階以上的導(dǎo)數(shù)統(tǒng)稱為高階導(dǎo)數(shù))二、高階導(dǎo)數(shù)1、定義機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分2、高階導(dǎo)數(shù)的運(yùn)算法則:機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束例1、解:高數(shù)導(dǎo)數(shù)與微分(1)函數(shù)的和、差、積、商的求導(dǎo)法則三、求導(dǎo)法則機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例1、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束練習(xí)1、高數(shù)導(dǎo)數(shù)與微分例如，(2)復(fù)合函數(shù)的求導(dǎo)法則機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束解：高數(shù)導(dǎo)數(shù)與微分例2、練習(xí)2、解:機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束解：高數(shù)導(dǎo)數(shù)與微分(3)隱函數(shù)求導(dǎo)法則機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例3、解：解得機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分練習(xí)3、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束解得高數(shù)導(dǎo)數(shù)與微分(4)參變量函數(shù)的求導(dǎo)法則機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例4、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分練習(xí)4、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分觀察函數(shù)求導(dǎo)方法——對(duì)數(shù)求導(dǎo)法：所屬類(lèi)型:先在方程兩邊取對(duì)數(shù),然后利用隱函數(shù)求導(dǎo)法求出導(dǎo)數(shù).(5)對(duì)數(shù)求導(dǎo)法機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例5、解：等式兩邊同時(shí)取對(duì)數(shù)得機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例6、解：等式兩邊同時(shí)取對(duì)數(shù)得機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分練習(xí)題：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分1、問(wèn)題的提出:正方形金屬薄片受熱后面積的改變量.四、微分機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分2、微分的定義機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分3、導(dǎo)數(shù)與微分的關(guān)系4、微分的求法求法：計(jì)算函數(shù)的導(dǎo)數(shù),然后乘以自變量的微分.機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例1、解：練習(xí)1、解：機(jī)動(dòng)目錄上頁(yè)下頁(yè)返回結(jié)束高數(shù)導(dǎo)數(shù)與微分例2