已知f(x)是二阶可导的函数,y=e2f(x), A. e2f(x) B. e

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问题 已知f(x)是二阶可导的函数,y=e2f(x),A. e2f(x) B. e2f(x)f''(x)C. e2f(x)[2f'(x)] D.2e2f(x) {2[f'(x)]2+f''(x)}

选项

答案D

解析提示:计算抽象函数的复合函数的二次导数:S' =e2f(x) ? 2f'(x) = 2f'(x)e2f(x)S''=2[f''(x)e2f(x)) + f'(x)? e2f(x)? 2f'(x)]=2e2f(x) {2[f'(x)]2+f''(x)}
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