⑩天掌 Teaching Plan on Advanced Mathematics 高阶导数运算法则 设函数和具有n阶导数,则 1)(u±p))=()±p (2)(Cn)()=Cn (3)(v) (n) nIn =uy+nuy+ (n-2)。P u n(n-1)…(n-k+1) (n-k)3,(k) 1+…+Lv k! ∑Cn (3)称为莱布尼兹公式Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 高阶导数运算法则 ( ) ( ) (2) ( ) n n Cu = Cu 设函数u和v具有n阶导数,则 ( ) ( ) ( ) (1) ( ) n n n u  v = u  v ( ) ( ) 0 ( ) ( ) ( ) ( ) ( ) ( 1) ( 2) ! ( 1) ( 1) 2! ( 1) (3) ( ) n k k n k k n n k k n n n n n C u v u v uv k n n n k u v n n u v u v nu v − = − − − =  + + − − + +  −  = +  +   (3)称为莱布尼兹公式