Question

f(x)的导数等于[f (x)]^2,求f(x)的n阶导数

Answer 1

f'(x)=[f(x)]^2df(x)/[f(x)]^2=dx-1/f(x)=x+C,C为常量f(x)=-1/(x+C)=-(x+C)^(-1)f'(x)=(x+C)^(-2)f"(x)=-2*(x+C)^(-3).f(x)的n阶导数=-(-1)(-2)(-3)...(-n)(x+C)^(-n-1)=(-1)^(n+1) *n!*(x+C)^(-n-1)