x=2在某邻域内可导fx二阶可导吗

Question

如题所述

Answer 1

可导
对f'(x)求导,得：f"(x)=f'(x)e^f(x)
f"'(x)=f"(x)e^f(x)+f'(x)f'(x)e^f(x)
f'(2)=e^f(2)=e
f"(2)=f'(2)e^f(2)=e^2
f"'(2)=f"(2)e^f(2)+f'(2)f'(2)e^f(2)=e^2*e+e*e*e=2e^3