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Cos∧3x/2的导数

(cos∧3x/2)'=3cos^2(x/2)*(cosx/2)'=3cos^2(x/2)*(-sinx/2)*(x/2)'=-3/2cos^2(x/2)sinx/2

导数为 3[cos(3x)]^2* [cos3x]' *(3x)'=-9sin3x*[cos3x]^2 ^2表示平方的意思 望采纳

解:y=sin[cos^2(tan^3x)]的导数.符合函数求导,换元法:令t=tanx,u=t^3,v=cosu,m=v^2,y=sinmdy/dx=dy/dmxdm/dvxdv/duxdu/dtxdt/dx=cosmx2vx(-sinu)x3t^2xsecxtanx=-6xcos[(cos∧2(tg∧3x))]xcos(tan^3x)xsin(tan^3x)xtan^2xsecxtanx=-6cos[(cos∧2(tg∧3x))]xcos(tan^3x)xsin(tan^3x)xtan^3secx

这是复合函数y=u^2,u=cosv,v=3x所以y'=2u*u'=2cos3x*(cosv)'=2cos3x*(-sinv)*v'=-2sin3xcos3x*(3x)'=-3sin6x

y'=(cos3x+2)'(3x+2)' =-sin(3x+2)*3 =-3sin(3x+2)

y = cos^2 x y '== 2cos x.-sinx复合函数的求导先对y=x^2求导=2x 再对cosx求导=sinx

y=lin(cos(10+3x^2))的导数 y=cos3x+2的导数是多少? y=cos(3x+5)的导数 Y=cos(3x-π/4)的导数 【急】一道导数题 求y=sin∧2 cos(3x)的导数 求cos^3 (3x)的导数?

y=(arcsin(x/2)^2y'=2arcsin(x/2)*(1/2)*(1/√1-x^2/4) =2arcsin(x/2)/√(4-x^2)y=e^(-x) cos3xy'=-e^(-x)cos3x-e^(-x)*(3sin3x)y=(sinx)^2 *3xy'=2sinxcosx*3x+3(sinx)^2

6cos(pi-3x)sin(pi-3x),符合函数求导要逐层求,然后相乘.

y=cos(π-3x)=-cos3x y′ = -(-sin3x)* 3 = 3sin3x

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