數(shù)學(xué)：334函數(shù)的和差積商的導(dǎo)數(shù)-新課標(biāo)人教A版選修1-1ppt課件

1、函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)導(dǎo)導(dǎo) 數(shù)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)和差積商的導(dǎo)數(shù)和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)由定義求導(dǎo)數(shù)三步法）由定義求導(dǎo)數(shù)三步法）步驟步驟:);()() 1 (00 xfxxfy求增量;)()()2(00 xxfxxfxy算比值.lim)3(0 xyyx 求求極極限限注意注意: :0)()(0 xxxfxf函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)常見函數(shù)的導(dǎo)數(shù)公式：常見函數(shù)的導(dǎo)數(shù)公式：公式：公式：)(0為為常常數(shù)數(shù)CC )()(1Qnnxxnn公式：公式：xxcos)(sin公式：公式：xxsin)(cos公式：公式：還有必要

2、建立求導(dǎo)法則，若兩個(gè)函數(shù)的導(dǎo)數(shù)存在，還有必要建立求導(dǎo)法則，若兩個(gè)函數(shù)的導(dǎo)數(shù)存在，如何求這兩個(gè)函數(shù)的和，差，積，商的導(dǎo)數(shù)呢？如何求這兩個(gè)函數(shù)的和，差，積，商的導(dǎo)數(shù)呢？函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)若若u=u(x)，v=v(x)在在x處可導(dǎo)，那么處可導(dǎo)，那么vuvu )( 1.和和(或差或差)的導(dǎo)數(shù)的導(dǎo)數(shù)法則法則1 兩個(gè)函數(shù)的和兩個(gè)函數(shù)的和(或差或差)的導(dǎo)數(shù)的導(dǎo)數(shù),等于這兩個(gè)函數(shù)的導(dǎo)數(shù)等于這兩個(gè)函數(shù)的導(dǎo)數(shù)的和的和(或差或差),即即 根據(jù)導(dǎo)數(shù)的定義，可以推出可導(dǎo)函數(shù)四則運(yùn)算的根據(jù)導(dǎo)數(shù)的定義，可以推出可導(dǎo)函數(shù)四則運(yùn)算的求導(dǎo)法則求導(dǎo)法則函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)1.和和(或差或差

3、)的導(dǎo)數(shù)的導(dǎo)數(shù)vuvu )( )()()(xvxuxfy證明： )()()()(xvxuxxvxxuy )()()()(xvxxvxuxxuvuxvxuxyxvxuxvxuxyxxxx0000limlimlimlim)()(xvxu函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)的導(dǎo)數(shù)求例xxysin. 13的導(dǎo)數(shù)求例3. 224xxxy函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)2.積的導(dǎo)數(shù)積的導(dǎo)數(shù)法則法則2 兩個(gè)函數(shù)的積的導(dǎo)數(shù)兩個(gè)函數(shù)的積的導(dǎo)數(shù),等于第一個(gè)函數(shù)的導(dǎo)數(shù)乘第二等于第一個(gè)函數(shù)的導(dǎo)數(shù)乘第二個(gè)函數(shù)個(gè)函數(shù),加上第一個(gè)函數(shù)乘第二個(gè)函數(shù)的導(dǎo)數(shù)加上第一個(gè)函數(shù)乘第二個(gè)函數(shù)的導(dǎo)數(shù),即即vuvuvu )( )

4、()()(xvxuxfy證明：)()()()(xvxuxxvxxuy)()()()()()()()(xvxuxxvxuxxvxuxxvxxuxxvxxvxuxxvxxuxxuxy)()()()()()(從而時(shí)，于是當(dāng)處連續(xù)，處可導(dǎo)，所以它在點(diǎn)在點(diǎn)因?yàn)?.()(0)(xvxxvxxxxv函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)xxvxxvxuxxvxxuxxuxyxxx)()(lim)()()()(limlim000)()()()(xvxuxvxu)(uvvuuvy即uCCu )( :推論函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)的導(dǎo)數(shù)求例4532. 322xxxy的導(dǎo)數(shù)求例)23)(32(. 42xxy函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商的導(dǎo)數(shù)3.商的導(dǎo)數(shù)商的導(dǎo)數(shù)法則法則3 兩個(gè)函數(shù)的商的導(dǎo)數(shù)兩個(gè)函數(shù)的商的導(dǎo)數(shù),等于分子的導(dǎo)數(shù)與分母的積等于分子的導(dǎo)數(shù)與分母的積,減減去分母的導(dǎo)數(shù)與分子的積去分母的導(dǎo)數(shù)與分子的積,再除以分母的平方再除以分母的平方,即即)0()(2vvvuvuvu的導(dǎo)數(shù)例xxysin. 52xxxxxy222sin)(sinsin)(解：xxxxx22sincossin2函數(shù)的和差積商的導(dǎo)數(shù)函數(shù)的和差積商