已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f（x)f'(x)+f^2(x)的值域是求当x属于【0，π/2】
问题描述：
已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.
已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f（x)f'(x)+f^2(x)的值域
是求当x属于【0，π/2】
答
f'(x)=cosx- sinx 最小正周期为2π
y-f'(x) =2sinx 最小正周期为2π
F(x)=f（x)f'(x)+f^2(x) =cos2x +sin2x +1
=根号2* sin(2x+π/4) +1 x∈[0, π/2], 2x+π/4 ∈[π/4, 5π/4]
F(x)的值域为[0, 1+根号2]
答
f(x) = sinx+cosxf'(x) = cosx -sinx= √2((1/√2)cosx - (1/√2)sinx)= √2(cos(x+π/4))f'(x) 的最小正周期 = 2πy-f'(x)=sinx+cosx -(cosx-sinx)=2sinxy-f'(x) 的最小正周期 = 2πF(x)= f(x)f'(x)+[f(x)]^2=(sinx...