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求导数技巧：隐函数求导法+对数求导法
在这个视频中, 我们讲解一道隐函数求导结合对数求导法的导数计算问题. 1. 通过求导法则, 将隐函数求导问题转变为两个幂指函数的求导问题. 2. 利用对数求导法(指数式)将幂指函数求导问题转换为复合函数求导问题. 3. 整理得到 y' 的表达式, 并将x=3, y=2代入得到答案. 在整个求导过程中, 要持续注意到 y 是 x 的函数, 与y有关的项的求导, 都要进行到 y' 为止.
高等数学(上)习题集62/264
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App08:43![求积分技巧之凑微分法(2), 最基础也是最重要的求积分方法[087]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9de6447729cb4290a20668a0693a96a6~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=XneGzb6fN1ocZrQN2Bkf2ukx%2FTM%3D)
App07:58![求积分技巧之分部积分法; 三指幂对反, 顺序不能忘[088]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/b2cd6ade410a4c14b8075e354d01110c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=wgeCAZPyO%2Btz9YBwrVXwtkg%2F3hg%3D)
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App11:49![根号? 根号! 换掉它! 根式代换 [092]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/911fb0cbd92441f5a7134c6854171552~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=y4f47GUD4QU%2BijB5HlJr9NmTsMA%3D)
App09:58![根式代换就是替换掉不易求解的根号部分 [093]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2f5944aa6d734c3d96a519c34f127c88~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=v0TPDjnTgFWJqKn%2Fr%2BgMmL%2BQPqo%3D)
App09:06![两道解题思路不拐弯的积分题|第二类换元法|裂项求积 [094]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/51fe2817a9f14283b33219e7901dc016~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=Q0GjPCMbey%2F1Dz7bDbsz0VdxFeg%3D)
App08:35![根式代换与三角代换都可以求解的两道题 [095]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/f040bca229ed4f94a33f87c1f89d2ceb~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=0r7kYj69Ez3h6UrSDiSEvZaUWaw%3D)
App06:08![三角代换能解的题, 我根式代换也想试一试[096]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/200afc81ad974f40be25d1e14e04a8c2~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=bR1pL0qd49EY41ZU%2FhA0cWR151c%3D)
App05:21![好吧, 这里居然是用分部积分[097]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8a61e746eb044856b425d15b515eb765~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=551qN4ghlEcsuB70f7yZ%2BEPH5NM%3D)
App06:05![凑微分嘛! 没有就构造[098]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/34bbb99701004974983f85acc5b98194~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=PexE79RuySShzY6nM0Xmx6uc6iY%3D)
App04:23![一种常见的凑微分方式: 硬凑! 积分嘛, 不寒碜[099]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/9008b820b68e44d5b6217aebbee651bd~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=OwwdoVyeQTUV8B2bM8wvgjidQ%2FE%3D)
App04:58![[100]两种方法求解, 难度差很大](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/7d2f088e942848438d530894bda7571d~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=2i9mGuuFRzceOInDvroc9SxclC4%3D)
App14:01![[101]有趣的换元方式; 拆项后将某一部分积分转化为所求积分](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/4f81bf6fb9ba4d1f8280c04bf57c2b7c~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=nkyjPzD06uWjO1WdrxRwONqFOeg%3D)
App03:51![[102]不用费曼积分法也能求.](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/edac18a3965a4d478b0fa1d4a22d656f~tplv-pk90l89vgd-crop-center:576:324.jpeg?appId=3586&biz_tag=list_custom%2Fnone&channelId=0&customType=custom%2Fnone&from=704_middle_image&imageType=list&isImmersiveScene=0&is_ios=1&is_stream=0&lk3s=9d3f5bff&logId=202503131634059A9AA4F3DEF0B0748C42&requestFrom=704&version_code=80402&x-expires=1773390845&x-signature=9lF2lZRZWM6h4iGY55PCata6aA4%3D)
App05:18
