大一高等數(shù)學(xué)教材2-3(存儲(chǔ)版)
【正文】 ????? yy Iax?特別地 .1)( ln xx ??二、復(fù)合函數(shù)的求導(dǎo)法則 定理 ).()(,)]([,)()(,)(0000000xufdxdyxxfyxuufyxxuxx? ????????????且其導(dǎo)數(shù)為可導(dǎo)在點(diǎn)則復(fù)合函數(shù)可導(dǎo)在點(diǎn)而可導(dǎo)在點(diǎn)如果函數(shù)即 因變量對(duì)自變量求導(dǎo) ,等于因變量對(duì)中間變量求導(dǎo) ,乘以中間變量對(duì)自變量求導(dǎo) .(鏈?zhǔn)椒▌t ) 證 ,)( 0 可導(dǎo)在點(diǎn)由 uufy ? )(l i m 00 ufuyu???????)0lim()( 00 ?????? ?? ?? uufuy故uuufy ?????? ?)( 0則xyx ????? 0lim ])([lim 00 xuxuufx ????????? ?xuxuufxxx ?????????????? 0000 limlimlim)().()( 00 xuf ? ???推廣 ),(),(),( xvvuufy ?? ???設(shè).)]}([{dxdvdvdududydxdyxfy???? 的導(dǎo)數(shù)為則復(fù)合函數(shù) ??例 3 .s i nln 的導(dǎo)數(shù)求函數(shù) xy ?解 .s i n,ln xuuy ???dxdududydxdy ??? xu co s1 ??xxsincos? xcot?例 4 .)1( 102 的導(dǎo)數(shù)求函數(shù) ?? xy解 )1()1(10 292 ????? xxdxdyxx 2)1(10 92 ??? .)
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