cos^2(1⼀x)的导数怎么求类似的呢

2025-04-07 19:34:55
推荐回答(1个)
回答1:

将1/x看做是v,将cos(1/x)看做是u:
原式 = cos²v = u²
根据分步求导:
(u²) = 2u* u′
= 2cosv * (cosv)′
= 2cosv * (-sinv) * v′
= -sin(2v) * v′
= -sin(2/x) * (1/x)′
= -sin(2/x) * (-1/x²)
= sin(2/x) / x²