来自葛杏卫的问题
已知:f(x+y)=f(x)+f(y)+xy(x+y),且f’(0)=1,求f(x).
已知:f(x+y)=f(x)+f(y)+xy(x+y),且f’(0)=1,求f(x).
1回答
2020-05-1213:26
已知:f(x+y)=f(x)+f(y)+xy(x+y),且f’(0)=1,求f(x).
已知:f(x+y)=f(x)+f(y)+xy(x+y),且f’(0)=1,求f(x).
答案是x+(1/3)x^3等式两边求导f'(x+y)(1+y')=f'(x)+f'(y)y'+y(x+y)+xyy'(x+y)+xy(x+y)(1+y')令x=0f'(y)(1+y')=1+f'(y)y'+y^2故f'(y)=1+y^2积分知f’(x)=x+(1/3)x^3