y=e^f(x),求y的三阶导数

2024-12-21 18:50:06
推荐回答(1个)
回答1:

三阶导数如下:
y=e^f(x)
y'=e^f(x)×f'(x)
y"=e^f(x)×f'(x)^2+e^f(x)×f"(x)
=e^f(x)[f'(x)^2+f"(x)]
y"'=e^f(x)f'(x)[f'(x)^2+f"(x)]+e^f(x)[2f'(x)f"(x)+f"'(x)]
y"'=e^f(x)[f'(x)^3+3f'(x)f"(x)+f"'(x)]