y=(cosx)三次方,,求Y的N次求导...追50分,如题...3/4 COS(X+N PI/2)+(3/4)^N COS (3X+N PI/2)
问题描述：
y=(cosx)三次方,,求Y的N次求导...追50分,
如题...
3/4 COS(X+N PI/2)+(3/4)^N COS (3X+N PI/2)
答
y'=3(cosx)^2*(-sinx)
(sinx)(n)=sin(x+(n*Pi)/2)
(cosx)(n)=cos(x+(n*Pi)/2)
y(n)=(3/4)*coc(x+n*Pi/2)+(3/4)^n*cos(3x+n*Pi/2)
y(n)表示函数f(x)的n阶导数
答
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答
cos3x = 4(cosx)^3 - 3cosxy = (cosx)^3 = 1/4 * (cos3x) + 3/4 * cosx(cosx)' = -sinx = cos(x+Pi/2)(cosx)'' = - cosx = cos(x+2*Pi/2)(cosx)n次导 = cos(x + n * Pi/2)y(n次导) = 3/4 * cos(x + n*Pi/2) + 1/4 * ...
答
y(n)=(3/4)*coc(x+n*Pi/2)+(3/4)^n*cos(3x+n*Pi/2)