xcxd.net
当前位置:首页 >> Cos^6x求导 >>

Cos^6x求导

-6sin6x ,复合函数求导,f(g(x))'=f'(x)*g'(x)

[(cosx)^6]' =6(cosx)^5·(-sinx) =3sin2x(cosx)^4

求导步骤如上图。

sin^6x+cos^6x =(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2xcos^2x) =sin^4x+cos^4x-sin^2xcos^2x =(sin^2x+cos^2x)^2-3sin^2xcos^2x =1-3sin^2xcos^2x =1-3/4·(sin2x)^2 =5/8+3/8·cos4x 所以,n阶导数为 3/8·4^n·cos(4x+nπ/2)

f(x) = (sinx)^6 + (cosx)^6 f'(x) = 6(sinx)^5 cosx - 6(cosx)^5 (sinx) = 6sinxcosx [(sinx)^4 - (cosx)^4] = 3sin2x [(sinx)^2 - (cosx)^2] = 3sin2xcos2x = (3/2)sin4x f''(x) = (3/2)4cos4x = (3/2)4sin(4x+π/2) f'''(x) = -(3/2)4^2 sin4x...

网站首页 | 网站地图
All rights reserved Powered by www.xcxd.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com