F(x)=f(cos²x)+f(sin²x),f 可导,令 u=cos²x,v=sin²x,则
du/dx = 2 cosx * (-sinx) = - sin(2x),dv/dx = 2 sinx * cosx = sin(2x)
F' (x) = f '(u) * du/dx + f '(v) * dv/dx
= sin(2x) * [ - f '(u) + f '(v) ]
= .答案是这样:F' (x) =-f(cos²x)* 2 cosx * (-sinx) +f(sin²x)* 2 sinx * cosx 我不知道前面为什么有负号?还有为什么还要写上f(cos²x) 、 f(sin²x)复合函数求导。du/dx = 2 cosx * (-sinx) = - sin(2x), dv/dx = 2 sinx * cosx = sin(2x)F ' (x) =sin(2x) * [ - f '(cos²x) +f '(sin²x) ] 或 F ' (x) = f ' (cos²x)* 2 cosx * (-sinx)+ f ' (sin²x) * 2 sinx * cosx 都正确。
F(x)=f(cos~2x)+f(sin~2x)的导数 急————————
F(x)=f(cos~2x)+f(sin~2x)的导数 急————————
数学人气:190 ℃时间:2019-11-06 20:34:08
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