设函数f(x)=cos(√3x+φ)(0﹤φ﹤π)．若f(x)+f′(x)是奇函数，则φ=____．

设函数f(x)=cos(√3x+φ)(0﹤φ﹤π)．若f(x)+f′(x)是奇函数，则φ=____．
【正确答案】：π/6。f(x)+f′(x)=cos(√3x+φ)-√3sin(√3x+φ)=2c0s(√3x+φ+π/3)，f(x)+f′(x)为奇函数，故f(0)+f′(0)=0，从而φ+π/3=π/2，φ=π/6．