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82问答网 > 计算y=cos(X)^(sin(x))的导数，求详解

计算y=cos(X)^(sin(x))的导数，求详解

2025-03-16 23:59:35

推荐回答（2个）

回答1：

这种题一般都是用对数法：
两边取对数： lny=sinxln(cosx)
方程两边对x求导，要把y看成是x的复合函数：
y'/y=(sinx)'ln(cosx)+sinx/cosx*(cosx)'
y'/y=cosxln(cosx)-sinx/cosx*sinx
y'=y[cosxln(cosx)-sinx tanx]
再代回y,也就是y'=(cosx)^(sinx) [cosxln(cosx)-sinx tanx]

回答2：

供参考：

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