求导函数：已知函数f(x)=2cos^2(3x-π/6)则函数f(x)在x=π/12处的导数fˊ(π/12)=?
问题描述：
求导函数：已知函数f(x)=2cos^2(3x-π/6)则函数f(x)在x=π/12处的导数fˊ(π/12)=?
答
f(x) =2cos²(x+π/12)+2sinxcosx-3 两倍角公式 2cos²(x+π/12)=1+cos2(x+π/12) =1+cos(2x+π/6)+sin2x-3 =cos2x*cosπ/6-sin2x*sinπ/6+sin2x-2 =cos2x*√3/2-sin2x*1/2+sin2x-2 =√3/2cos2x+1/2sin2x-2 =sin(2x+π/3)-2 T=2π/2=π
答
先求导,fˊ(x)=-12cos(3x-π/6)sin(3x-π/6)=-6sin(6x-π/3)
带入数值：fˊ(π/12)=-6sin(π/2-π/3)=-3