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Cos^6x求导

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

方法1y=sin²(3x)y=1/2*(1-cos6x)=1/2-(1/2)cos6xdy/dx=-1/2*d(cos6x)/d(6x)*d(6x)/dx=-1/2*(-sin6x)*6=3sin6x 方法2:直接用链式法则y=sin²(3x)dy/dx=d[sin(3x)]²/d[sin(3x)]*d[sin(3x)]/d(3x)*d(3x)/dx=2sin(3x)*cos(3x)*3=6sin(...

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...

y'=8sin^7x cosx-8cos^7x sinx=8sinxcosx(sin^6x-cos^6x)=4sin2x(sin^6x-cos^6x) 由y'=0,得:sin2x=0或sin^6x-cos^6x=0 得:x=kπ/2或 x=kπ+π/4 x=kπ/2左右邻域时,y'符号从正到负,因此为极大值点:y=1 x=kπ+π/4左右邻域时,y'的符号从负到正,...

∫x^2sin^2xdx =1/2∫x^2(1-cos2x)dx =1/2∫x^2dx-1/2∫x^2cos2xdx =1/6x^3-1/4∫x^2dsin2x =1/6x^3-1/4x^2sin2x+1/4∫2xsin2xdx =1/6x^3-1/4x^2sin2x-1/4∫xdcos2x =1/6x^3-1/4x^2sin2x-1/4xcos2x+1/4∫cos2xdx =1/6x^3-1/4x^2sin2x-1/4xcos2x+1/8sin2x...

=[1/(-6x^2+7x+3)]*(-12x+7)=(7-12x)/(-6x^2+7x+3).y=sin^2x+cos^4x此题和函数和复合函数的综合求导,步骤为:y'=2sinx*(sinx)'+4cos^3x...

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