函数y=sin^7(54x^2+21x+16)的导数计算.docx

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1、函数y-sin7(54x221x+16)的导数计算主要内容：本文主要用复合函数求导法则、链式求导法则以及取对数求导等方法，介绍计算函数y=sir(542+21x+16)一阶和二阶导数的步骤。复合函数链式求导计算一阶导数由复合函数求导法则，对X求导有：7*sin2(54x1x16)*cos(54x21x16)*(54x21x16)=7*sin2(54x2+21x+16)*cos(54x2+21x+16)*(108x+21),-7(108x+21)*sin2(54x2+21x+16)*cos(54x2+21x+16).取对数求导计算一阶导数首先对方程两边取对数，有：Iny=1nsin7(54x2+

2、21x+16),Iny=7Insin(54x2+21x+16),方程两边同时对X求导，有：y7sin(54x2+21x+16),ysin(54x2+21x+16),y_7cos(54x2+21x+16)(108x+21)ysin(54x2+21x+16),t_sin7(54x2+21x+16)*7cos(54x2+21x+16)(108x+21)Vsin(54x2+21x+16),y=sin2(54x2+21x+16)*7cos(54x2+21x+16)(108x+21),=7(108x+21)sin2(54x2+21x+16)*cos(54x2+21x+16).二阶导数计算本处根据函数特征，

3、采取取对数计算导数，首先对函数两边同时取对数，有：Iny,=1n7(108x+21)Sin2(54x2+21x+16)*cos(54x2+21x+16),则:Iny,=1n7+In(108x+21)+61nsin(54x2+21x+16)Incos(54x2+21x+16),对方程两边同时对X再次求导，y1086sin(542+21x+16),cos(542+21x+16)y,108x+21+sin(54x2+21x+16)+cos(54x2+21x+16)1086cos(542+21x+16)(108x+21)_108x+21+sin(54x2+21x+16)sin(542+21x+16)(

4、108x+21)cos(54x2+21x+16)108、,2、1R+?1+6(18x+21)Ctg(54x+21x+16)-IJOJ*I(108x+21)tan(54x2+21x+16),5!J:08y,=7(108x+21)sin2(54x2+21x+16)*cos(54x2+21x+16)108+2+6(108x+21)ctg(54x2+21x+16)-(108x+21)tan(54x2+21x+16),=756sin2(54x2+21x+16)*cos(54x2+21x+16)+42(108x+21)2sin5(54x2+21x+16)*cos2(54x2+21x+16)-7(108x+21)2sin7(54x2+21x+16),=378sin5(54x2+21x+16)*sin(108x2+42x+32)+42(108x+21)2sin5(54221x+16)*cos2(54x2+21x+16)-7(108x+21)2sin7(54x2+21x+16)。