清華微積分高等數(shù)學(xué)課件第六講導(dǎo)數(shù)與微分二(參考版)
2025-01-19 06:42本頁(yè)面
【正文】 )()]([ ???的函數(shù)，微分形式不變還是中間變量是自變量不論 uxy但有 微分的 形式不變性 2022/2/13 14 .11]1[23的導(dǎo)數(shù)求函數(shù)例 ?????????xxy[解 ] ??????????????????111123 21xxdxdxxdxdy221)1(21123???????????xxx2521)1()1(3???xx2022/2/13 15 42,ln?????xvt gvuuy設(shè)xvuxxt gvuy )42()()(l n ?????????.)]42l n [t an (]2[ 的導(dǎo)數(shù)求函數(shù)例 ??? xy[解 ] 21c o s112 ??? vu21)(c os1)(142242??????? xxtg)s i n (12???x xc o s1?xse c?2022/2/13 16 .)1l n (]3[ 2 的導(dǎo)數(shù)求函數(shù)例 ??? xxyxx xxxxy )1(11 22????????1111112222 ?????????xxxxxx])1(1[11 22 xxxx???????[解 ] ])1(1211[11 222 xxxxx?????????2022/2/13 17 .ln]4[ 的導(dǎo)數(shù)求函數(shù)例 xy ?????????時(shí)當(dāng)時(shí)當(dāng)0,)l n (0,lnlnxxxxxyxxyx 1)(l n,0 ????? 時(shí)當(dāng)])[ l n (,0 ????? xyx 時(shí)當(dāng))0(1)(l n ???? xxxxxx1)(1 ??????[解 ] .lnln同的導(dǎo)數(shù)公式有相與 xx)()(])([l n])([l nxfxfxfxf ?????2022/2/13 18 .,]1[中間變量都便于求導(dǎo)應(yīng)使每一個(gè)地選取中間變量恰當(dāng)在于分析清楚函數(shù)關(guān)系關(guān)鍵：復(fù)合函數(shù)求導(dǎo)數(shù)時(shí)注意.,]2[就用什麼求導(dǎo)法則什麼運(yùn)算碰到四則運(yùn)算的函數(shù)關(guān)系時(shí)又有：當(dāng)
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