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y sin4x Cos4x

原式=分母为(sin^4x)'(4+cos^4x)-sin^4X(4+COS^4X)'分子为(4+cos^4x)^2 其中sin^4x的导数为4sin^3xcosx,而4+cos^4x的导数为-4cos^3xsinx

y=sin^4(x/4)+cos^4x y'=4sin^3(x/4)*cos(x/4)*(1/4)-4cos^3x*sinx =sin^3(x/4)*cos(x/4)-4sinx*cos^3x

解y′=(sin4x)′ =cos4x*(4x)′ =4*cos4x

∵y=sin4x+cos4x=(sin2x+cos2x)2-2sin2xcos2x=1-12×sin22x=1-12×1?cos4x2=34+14×cos4x,∴其周期T=2π4=π2,故答案为:π2.

因为cosz=sin(pi/2+z) 所以y=cos(4x+pi/6)=sin(pi/2+4x+pi/6)=sin(4x+2/3*pi)=sin[4(x+pi/6)] 故应是向右平移pi/6个单位。

Y=sin^4x+cos^2x =(sin²x)²-sin²x+1 =[sin²x-1/2]²+3/4 =(1/4)cos²2x+3/4 最小正周期为 2π/2=π

cos4x-sin2x=1-2sin²2x-sin2x

y=√2sin(4x+π/4) g(x)=√2sin[4(x-π/8)+π/4]+1 =√2sin(4x-π/4)+1 0≤x≤π/4 -π/4≤4x-π/4≤3π/4 f(x)min=0 f(x)max=√2+1

应该是y=-1/4cos4x+C

平方差公式,然后两角和公式 [-1,1]

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