清華大學(xué)微積分高等數(shù)學(xué)課件第6講導(dǎo)數(shù)與微分二-閱讀頁(yè)
2025-01-31 06:20本頁(yè)面
【正文】 .s e cc os1c os)s i n(s i nc osc os222xxxxxxx???????的導(dǎo)數(shù)求函數(shù)例 xxf t a n)(]8[ ?[解 ] xxx22c o s1s e c)( t a n???2022/2/13 8 復(fù)合函數(shù)導(dǎo)數(shù)公式 （ 1）復(fù)合函數(shù)微分法（鏈?zhǔn)椒▌t） 且也可導(dǎo)在點(diǎn)則復(fù)合函數(shù)可導(dǎo)在點(diǎn)函數(shù)可導(dǎo)在點(diǎn)設(shè)函數(shù),)]([,)(,)(xxgfyxxguuufy???dxdududydxdy??或)()]([)]([ xgxgfdxxgdf ????2022/2/13 9 [證 ] xyx ??? 0l i m???????????????????? ????? xuuyxuuyxux ??????????? 000limlimlimdxdududy ?? )())(( xgxgf ???0,0 ?? xx ?? 時(shí)當(dāng)不能保證中間變量的增量 )()( xgxxgu ??? ??總不等于零 上面的證法有沒有問題？ 2022/2/13 10 [證 ] ?? 可導(dǎo))( ufy??? ???? )( ufuy )0lim(0 ?? ?? u)(lim0ufuyu??? ???上式化為時(shí)當(dāng) ,0?u?)1()( uuufy ???? ?????0)()(,0 ????? ufuufyu ??? 時(shí)當(dāng)(1) 式仍然成立！ xuxuufxy??????? ?????? )(2022/2/13 11 xuxuufxyxxxx ??????????? 0000l i ml i ml i m)(l i m??????????)()(lim)]([0xgufxydxxgdfx??????? ???0l i ml i m 00 ??? ?? ?? ?? ux)()()](([ xgufdxxgfd ?????連續(xù)可導(dǎo) )()( xguxgu ???00 ??? ux ??2022/2/13 12 （ 2）微分的形式不變性 (復(fù)合函數(shù)微分法則 ) 且其微分為也可微則復(fù)合函數(shù)函數(shù)均為可微和設(shè)函數(shù),)]([,)()(xgfyxguufy???dxxuufduufdy )(39。)(39。
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