作业帮数学函数求导
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/13 04:20:17
数学函数求导
y=sinaxcosbx=(1/2)[sin(a+b)x+sin(a-b)x]
y'=(1/2)[(a+b)cos(a+b)x+(a-b)cos(a-b)x]
y"=-(1/2)[(a+b)^2sin(a+b)x+(a-b)^2sin(a-b)x]
y(3)=-(1/2)[(a+b)^3cos(a+b)x+(a-b)^3cos(a-b)x]
y(4)=(1/2)[(a+b)^4sin(a+b)x+(a-b)^4sin(a-b)x]
y(n)导数可分四种不同表达式
n=4m时,(m=1,2,3,...)
y(n)=(1/2)[(a+b)^n*sin(a+b)x+(a-b)^n*sin(a-b)x]
n=4m-1时,
y(n)=-(1/2)[(a+b)^n*cos(a+b)x+(a-b)^n*cos(a-b)x]
n=4m-2时,
y(n)=-(1/2)[(a+b)^n*sin(a+b)x+(a-b)^n*sin(a-b)x]
n=4m-3时
y(n)=(1/2)[(a+b)^n*cos(a+b)x+(a-b)^n*cos(a-b)x]
y'=(1/2)[(a+b)cos(a+b)x+(a-b)cos(a-b)x]
y"=-(1/2)[(a+b)^2sin(a+b)x+(a-b)^2sin(a-b)x]
y(3)=-(1/2)[(a+b)^3cos(a+b)x+(a-b)^3cos(a-b)x]
y(4)=(1/2)[(a+b)^4sin(a+b)x+(a-b)^4sin(a-b)x]
y(n)导数可分四种不同表达式
n=4m时,(m=1,2,3,...)
y(n)=(1/2)[(a+b)^n*sin(a+b)x+(a-b)^n*sin(a-b)x]
n=4m-1时,
y(n)=-(1/2)[(a+b)^n*cos(a+b)x+(a-b)^n*cos(a-b)x]
n=4m-2时,
y(n)=-(1/2)[(a+b)^n*sin(a+b)x+(a-b)^n*sin(a-b)x]
n=4m-3时
y(n)=(1/2)[(a+b)^n*cos(a+b)x+(a-b)^n*cos(a-b)x]