高數(shù)微積分公式大全

高等數(shù)學微積分公式大全一、基本導數(shù)公式⑴SKIPIF1<0⑵SKIPIF1<0⑶SKIPIF1<0⑷SKIPIF1<0⑸SKIPIF1<0⑹SKIPIF1<0⑺SKIPIF1<0⑻SKIPIF1<0⑼SKIPIF1<0⑽SKIPIF1<0⑾SKIPIF1<0⑿SKIPIF1<0⒀SKIPIF1<0⒁SKIPIF1<0⒂SKIPIF1<0⒃SKIPIF1<0⒄SKIPIF1<0⒅SKIPIF1<0二、導數(shù)的四則運算法則SKIPIF1<0SKIPIF1<0SKIPIF1<0三、高階導數(shù)的運算法則（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0四、基本初等函數(shù)的n階導數(shù)公式（1）SKIPIF1<0（2）SKIPIF1<0(3)SKIPIF1<0(4)SKIPIF1<0(5)SKIPIF1<0(6)SKIPIF1<0(7)SKIPIF1<0五、微分公式與微分運算法則⑴SKIPIF1<0⑵SKIPIF1<0⑶SKIPIF1<0⑷SKIPIF1<0⑸SKIPIF1<0⑹SKIPIF1<0⑺SKIPIF1<0⑻SKIPIF1<0⑼SKIPIF1<0⑽SKIPIF1<0⑾SKIPIF1<0⑿SKIPIF1<0⒀SKIPIF1<0⒁SKIPIF1<0⒂SKIPIF1<0⒃SKIPIF1<0六、微分運算法則⑴SKIPIF1<0⑵SKIPIF1<0⑶SKIPIF1<0⑷SKIPIF1<0七、基本積分公式⑴SKIPIF1<0⑵SKIPIF1<0⑶SKIPIF1<0⑷SKIPIF1<0⑸SKIPIF1<0⑹SKIPIF1<0⑺SKIPIF1<0⑻SKIPIF1<0⑼SKIPIF1<0⑽SKIPIF1<0⑾SKIPIF1<0八、補充積分公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0九、下列常用湊微分公式積分型換元公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0十、分部積分法公式⑴形如SKIPIF1<0，令SKIPIF1<0，SKIPIF1<0形如SKIPIF1<0令SKIPIF1<0，SKIPIF1<0形如SKIPIF1<0令SKIPIF1<0，SKIPIF1<0⑵形如SKIPIF1<0，令SKIPIF1<0，SKIPIF1<0形如SKIPIF1<0，令SKIPIF1<0，SKIPIF1<0⑶形如SKIPIF1<0，SKIPIF1<0令SKIPIF1<0均可。十一、第二換元積分法中的三角換元公式(1)SKIPIF1<0SKIPIF1<0(2)SKIPIF1<0SKIPIF1<0(3)SKIPIF1<0SKIPIF1<0【特殊角的三角函數(shù)值】（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0）（5）SKIPIF1<0（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0）（5）SKIPIF1<0（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0不存在（5）SKIPIF1<0（1）SKIPIF1<0不存在（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0（5）SKIPIF1<0不存在十二、重要公式（1）SKIPIF1<0（2）SKIPIF1<0（3）SKIPIF1<0（4）SKIPIF1<0（5）SKIPIF1<0（6）SKIPIF1<0（7）SKIPIF1<0（8）SKIPIF1<0（9）SKIPIF1<0（10）SKIPIF1<0（11）SKIPIF1<0（12）SKIPIF1<0（系數(shù)不為0的情況）十三、下列常用等價無窮小關系（SKIPIF1<0）SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0十四、三角函數(shù)公式1.兩角和公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<02.二倍角公式SKIPIF1<0SKIPIF1<0SKIPIF1<03.半角公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<04.和差化積公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<05.積化和差公式SKIPIF1<0SKIPIF1<0SKIPIF1<0SKIPIF1<06.萬能公式SKIPIF1<0SKIPIF1<0SKIPIF1<07.平方關系SKIPIF1<0SKIPIF1<0SKIPIF1<08.倒數(shù)關系SKIPIF1<0SKIPIF1<0SKIPIF1<09.商數(shù)關系SKIPIF1<0SKIPIF1<0十五、幾種常見的微分方程1.可分離變量的微分方程：SKIPIF1<0，SKIPIF1<02.齊次微分方程：SKIPIF1<03.一階線性非齊次微分方程：SKIPIF1<0解為：SKIPIF1<0一些初等函數(shù)：兩個重要極限：三角函數(shù)公式：·誘導公式：函數(shù)角Asincostgctg-α-sinαcosα-tgα-ctgα90°-αcosαsinαctgαtgα90°+αcosα-sinα-ctgα-tgα180°-αsinα-cosα-tgα-ctgα180°+α-sinα-cosαtgαctgα270°-α-cosα-sinαctgαtgα270°+α-cosαsinα-ctgα-tgα360°-α-sinαcosα-tgα-ctgα360°+αsinαcosαtgαctgα·和差角公式：·和差化積公式：·倍角公式：·半角公式：SKIPIF1<0·正弦定理：SKIPIF1<0·余弦定理：SKIPIF1<0·反三角函數(shù)性質：SKIPIF1<0高階導數(shù)公式——萊布尼茲（Leibniz）公式：SKIPIF1<0中值定理與導數(shù)應用：SKIPIF1<0微分方程的相關概念：SKIPIF1<0一階線性微分方程：SKIPIF1<0全微分方程：SKIPIF1<0二階微分方程：SKIPIF1<0二階常系數(shù)齊次線性微分方程及其解法：SKIPIF1<0SKIPIF1<0SKIPIF1<0(*)式的通解兩個不相等實根SKIPIF1<0SKIPIF1<0兩個相等實根SKIPIF1<0SKIPIF1<0一對共軛復根SKIPIF1<0SKIPIF1<0SKIPIF1<0二階常系