f(x)的导数等于[f (x)]^2,求f(x)的n阶导数

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f(x)的导数等于[f(x)]^2,求f(x)的n阶导数f(x)的导数等于[f(x)]^2,求f(x)的n阶导数f(x)的导数等于[f(x)]^2,求f(x)的n阶导数f''(x)=[f(x)]^2df

f(x)的导数等于[f (x)]^2,求f(x)的n阶导数
f(x)的导数等于[f (x)]^2,求f(x)的n阶导数

f(x)的导数等于[f (x)]^2,求f(x)的n阶导数
f'(x)=[f(x)]^2
df(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)

等于0吧