sin(x^2)=(1-cos2x)/2所以sin(x^2)的n阶导数为-1/2cos2x的n阶导数cosax的n阶导数=a^ncos(ax+n兀/2)所以sin(x^2)的n阶导数为-1/2*2^ncos(2x+n兀/2),你再将结果整理一下
y=(sinx)^3 y'=3(sinx)^2cosx=(3/2)(1-cos2x)cosx=(3/2)(cosx-cos2xcosx) cos2xcosx积化和差之后按如下规律计算 sin(ax)的n阶导数是a^n*sin(ax+(n/2)pi). cos(ax)的n阶导数是a^n*cos(ax+(n/2)pi). pi是圆周率.
y=sinx=(1/2)(1-cos2x) y'=(1/2)*2sin(2x)=sin(2x) y''=2cos(2x)=2sin(2x+π/2) y'''=-4sin(2x)=4sin(2x+π) y^(4)=-8cos(2x)=8sin(2x+3π/2) y^(5)=16sin(2x)=16sin(2x+2π).y^(n)=[2^(n-1)]sin(2x+(n-1)π/2) 希望可以帮到你,不明白可以追问,如果解决了问题,请点下面的＂选为满意回答＂按钮.
y'(0)=lim(t->0)[y(t)-y(0)]/t=lim(t->0)(sint/t-1)/t=0 当x≠0时,xy=sinx,y+xy'=cosx,y'(x)=(cosx-y)/x y''(0)=lim(t->0)[y'(t)-y'(0)]/t=lim(t->0)[cost-y(t)]/t^2=∞ 所以当n=1时,y'(0)=0,当n>=2时,y^(n)(0)不存在 扩展资料 二阶及二阶以上的导数统称为高阶导数.从
y=sinx的n阶导数?y=sinx=(1/2)(1-cos2x)y'=(1/2)*2sin(2x)=sin(2x)y''=2cos(2x)=2sin(2x+π/2)y'''=-4sin(2x)=4sin(2x+π)y^(4)=-8cos(2x)=8sin(2x+3π/2)y^(5)=16sin(2x)=16sin(2x+2π).y^(n)=[2^(n-1)]sin(2x+(n-1)π/2)希望能帮到你
y'=cosx=sin(x+pi/2)y''=-sinx=sin(x+pi)y'''=-cosx=sin(x+3pi/2)y''''=sinx=sin(x+2pi)yn'=sin(x+npi/2)
y(1)=cosxy(2)=-sinxy(3)=-cosxy(4)=sinxy(5)=cosx所以,周期为4即:y(n)=cosx n=4k+1,k∈Ny(n)=-sinx n=4k+2,k∈Ny(n)=-cosx n=4k+3,k∈Ny(n)=sinx n=4k+4 k∈N祝你开心!希望能帮到你,如果不懂,请追问,祝学习进步!O(∩_∩)O
y=sinxy'=cosx=sin(x+π/2)y''=-sinx=sin(x+2*π/2)y'''=-cosx=sin(x+3*π/2)所以:y(n)=sin(x+nπ/2),
4n+1阶cosx4n+2阶-sinx4n+3阶-cosx4n+4阶sinxn=0,1,2,3……
若n除以4余1,sin2x的n阶导数为2^n cos2x 若n除以4余2,sin2x的n阶导数为-2^n sin2x 若n除以4余3,sin2x的n阶导数为-2^n cos2x 若n能被4整除,sin2x的n阶导数为2^n sin2x 综合起来,sin2x的n阶导数为:2^nsin(2x+nπ/2)