名校
解题方法
1 . 我们把底数和指数同时含有自变量的函数称为幂指函数,其一般形式为
,幂指函数在求导时可以将函数“指数化"再求导.例如,对于幂指函数
,
.
(1)已知
,求曲线
在
处的切线方程;
(2)若
且
,
.研究
的单调性;
(3)已知
均大于0,且
,讨论
和
大小关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541b679b72673528f0e37bfeb6d1dff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46d3504fd4d99c1a9a293a9363256ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fc4b04f98545b403a28d41c6e109c4.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7395df460e74ac91beeb82f99bf301ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b91f5cf5a5fede52e96a0cb5ac079b.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607ea0d316d84b1ea5e6e735ac29b332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94933201271f9408e70cd2f2182f4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c632bdc4a2b1c4891d1cf5345571d23.png)
您最近一年使用:0次
名校
2 . 烧水时,水温随着时间的推移而变化.假设水的初始温度为
,加热后的温度函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a75c767798abfb5dcb88cd21dc4e64c.png)
(
是常数,
表示加热的时间,单位:min),加热到第10min时,水温的瞬时变化率是_________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2969d81e7c1cc013e2bc059ac498f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a75c767798abfb5dcb88cd21dc4e64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438cf67762709c13f3d15a1a91e8b2c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed3cc507657af0aa845cab1d8bd44d3.png)
您最近一年使用:0次
2023-12-23更新
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965次组卷
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