cos^2(x)的导数

{cos^3(3x)}'=3cos^2(3X){cos(3x)}'=3cos^2(3X){-sin(3x)}(3x)'=3cos^2(3X){-sin(3x)}3=-9sin(3x)cos^2(3x)

这是复合函数,f(x)=x^2g(x)=cosxh(x)=lnx所以f{g[h(x)]}=[cos(Inx)]^2所以首先对平方求导,再对cos求导,最后对ln求导所以f'(x)=2cos(lnx)*

y'=-sin[ln(1+2x)]×[ln(1+2x)]'=-sin[ln(1+2x)]×1/(1+2x)×(1+2x)'=-sin[ln(1+2x)]×1/(1+2x)×2=-2sin[ln(1+2

f(x)*f(y)的导数是f(x)的导数乘以f(y)+f(x)乘以f(y)的导数所以f(x)的导数是1-(1/2*cos(x/2)*cos(x/2)+sin(x/2)*(-sin(x/2))*1/2)

解析y=sinxsinxcosxy'=sinx'sinxcosx+sinx(sinxcosx)'=cosxsinx+sinx(sinx'cosx+sinxcosx')=cosxsinx+sinx(co

y=cos^2x+cosx^2y'=2cosx(-sinx)+(-sinx^2)*2x=-2sinxcosx-2xsinx^2=-sin2x-2xsinx^2

[cos(1+x)]=-sin(1+x)*(1+x)'=-sin(1+x)再问：如果是求cos(1+x^2)的导数？再答：属于复合函数。y=cos(1+x)可以设t=x+1，则dy/dt=-sint,

-2xsin(x^2)

(cos(3x))'=-sin(3x)*(3x)'=-3sin(3x)

y‘=[sin²(cos3x)]'=2sin(cos3x)×[sin(cos(3x))]'=2sin(cos3x)cos(cos(3x))(cos3x)'=sin[2(cos3x)]×(-s

cos(3-x)'=-sin(3-x)*(-1)=sin(3-x)

y=cos(x+2)y'=(x+2)'（-sin(x+2))=-sin(x+2)lim(△x→0)[cos(x+△x+2)-cos(x+2)]/[(x+△x+2)-(x+2)]=lim(△x→0)-2

根据复合函数求导法则,y'=(1/cos(3+2x^2))*ln10*(-sin(3+2x^2))*4x.整理一下就是y'=-4x*ln10*cot(3+2x^2)欢迎追问~再问：这个ln10怎么处理

先对cos求导=-sinx^2再对x^2求导=2x所以y'=-2x*cosx^2

因为sin[2*(x/2)]=2sin(x/2)cos(x/2)所以x-sin(x/2)cos(x/2)=x-1/2sinx导数为1-1/2cosx

-(2x+1)sin(x^2+x+1)再问：请问可以写一下过程么？再答：先导cos，cos的导数=-sin，然后导括号里面x^2+x+1，两部分乘起来

f'(x)=[(2-sinα)'cosα-(2-sinα)(cosα)']/cos²α=(-cos²α+2sinα-sin²α)/cos²α=(2sinα-1)

(x*sinx*cosx)'=(1/2xsin2x)'=1/2(sin2x+xcos2x*2)=1/2sin2x+xcos2x

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y'=3cos²x/2*-sinx/2*1/2=-3/2cos²x/2sinx/2