高等数学--导数概念

1、(2 ysh xech x (3 yth(ln x(4 ysh3x ch2x (5 yth(1x2 (6 yarch(x21(7 yarch(e2x(8 yarctan(th x(9(10解 (1 ysh(sh x(sh xsh(sh xch x (2 ych xech xsh xech xsh xech x(ch xsh2x (3 (4 y3sh2xch x2ch xsh x sh xch x(3sh x2 (5 (6 (7 (8 (9(10 12 求下列函数的导数 (1 yex(x22x3 (2 ysin2xsin(x2(3(4(5(6(7(8(9 (10解 (1 yex(x22x3ex(

2、2x2ex(x24x5 (2 y2sin xcos xsin(x2sin2xcos(x22xsin2xsin(x22xsin2xcos(x2 (3 (4 (5 (6 (7 (8(9 (10习题 231 求函数的二阶导数 (1 y2x2ln x(2 ye2x1(3 yxcos x (4 yet sin t (5(6 yln(1x2(7 ytan x(8(9 y(1x2arctan x (10(11(12 解 (1 (2 ye2x1 22e2x1 y2e2x1 24e2x1 (3 yxcos x ycos xxsin x ysin xsin xxcos x2sin xxcos x (4 yetsi

3、n tetcos tet(cos tsin tyet(cos tsin tet(sin tcos t2etcos t (5 (6 (7 ysec2 x y2sec x(sec x2sec xsec xtan x2sec2xtan x (8 (9 (10 (11 (12 2 设f(x(x106 f (2?解f (x6(x105 f (x30(x104 f (x120(x103 f (2120(2103207360 3 若f (x存在 求下列函数y的二阶导数 (1 yf(x2 (2 ylnf(x 解 (1y f (x2(x22xf (x2 y2f (x22x2xf (x22f (x24x2f (x

4、2 (2 4 试从导出 (1 (2 解 (1 (2 5 已知物体的运动规律为sAsint(A、是常数 求物体运动的加速度 并验证解 就是物体运动的加速度 6 验证函数yC1exC2ex(C1 C2是常数满足关系式y2y0 解 yC1exC2ex yC12exC22exy2y(C12exC22ex2(C1exC2ex(C12exC22ex(C12exC22ex0 7 验证函数yexsin x满足关系式y2y2y0 解 yexsin xexcos xex(sin xcos x yex(sin xcos xex(cos xsin x2excos x y2y2y2excos x2ex(sin xcos x2exsin x2excos x2exsin x2excos x2exsin x0 8 求下列函数的n阶导数的一般表达式 (1 yxna1xn1a2xn2 an1xan (a1 a2 an都是常数 (2 ysin2x (3 yxln x (4 yxex 解 (1 ynxn1(n1a1xn2(n2a2xn3 an1 yn(n1xn2(n