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Cos^6x求导

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

-6sin6x ,复合函数求导,f(g(x))'=f'(x)*g'(x)

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,...

y=sin²3x+5cosx² y'=(2sin3x)*(cos3x)*3-5(sinx²)*(2x) =3sin6x-10xsinx² 如果题目为 y=sin²3x+5cos²x y'=(2sin3x)*(cos3x)*3-5*(2cosx)(sinx) =3sin6x-5sin2x

1.y'=2cos(3x-r)*3*-sin(3x-r)=-6cos(3x-r)sin(3x-r)=-3sin6x 2.求导,y'=2x-1/x*x y'

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...

∫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...

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