已知f(x)是二阶可导的函数,y=e2f(x),则dy2/dx2为:
2023-06-07
A. e2f(x)
B. e2f(x)f''(x)
C. e2f(x)[2f'(x)]
D.2e2f(x) {2[f'(x)]2+f''(x)}
参考答案:D
B. e2f(x)f''(x)
C. e2f(x)[2f'(x)]
D.2e2f(x) {2[f'(x)]2+f''(x)}
参考答案:D
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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