设函数f(x)在x=2的某领域内可导，且f'(x)=e^f(x),f(2)=1,求f'''(2)的值

Question

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Answer 1

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