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[高等数学13]如何理解微分？
高等数学合集13/44
![[高等数学11]导函数的概念＆基本初等函数导数公式证明](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/cdc442e692724b83b411ec1f0fdc36a5~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=UyKA%2FJhN7h5itrAi8ujWfWquDYs%3D)
App21:41![[高等数学13]如何理解微分？](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/a2e0de967ce7448db9f799b79ec8bd6c~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=DNts79Nl7mQc9SHFFgnZ3DZ%2FRKc%3D)
App20:26![[高等数学14]罗尔中值定理——微分中值定理1](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/0dd23ce323604df4a87c0667566d4e2d~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=IH9u0YU2es35wM5qGt4hDJjlRj0%3D)
App15:41![拉格朗日中值定理[高等数学15]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/3a98032c3fb24c2d99861489d679f061~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=iCC2SnpMozCZbyAkUWAX1J9g6uo%3D)
App20:47![[高等数学16]柯西中值定理](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/f5d1aed39d4f4b369461c2e9aa6e7395~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=4Tth9O0%2FwnKgS%2BIz0oS66DhiQ%2F4%3D)
App11:23![洛必达法则[高等数学17]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/02cb1d84c0fc4ac68f45fc5bc2ac2b5f~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=ufY2YJ58u5llsgB2ZTsIWellzGI%3D)
App21:09![泰勒公式及麦克劳林公式[高等数学18]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/4960df96913d4e95827aea2c843d5168~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=gWo94R3tdXXV9%2BRBrSbquAPI2nc%3D)
App15:24![泰勒公式的正确打开方式[高等数学19]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2359e6b0942345a89a6297704294549f~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=zeJ4l77uylH4rpGkwjLr1hDBCgE%3D)
App10:09![函数的凹凸性[高等数学20]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2bccdf5604834d139776bd5cd6d0b198~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=8bZEchyOPNtawpZU6DafRxhDg3o%3D)
App14:58![不定积分[高等数学21]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/2d430c39d9c54b4483d0eefb2d092179~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=ZR55ow4wNl%2BlWGXBCUWMzSadbHo%3D)
App18:06![换元积分法，第一换元法＆第二换元法[高等数学22]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/b7afa697793c4b1282bea0e02a6e9930~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=R6WS4lM0xrSGgnnKpnEQK2%2FAOxo%3D)
App15:13![分部积分法[高等数学23]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/083f53d7b0ae43b8847f19fcbc9f394f~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=qYH2VIVip4JasnV9W5RiRfUpeOs%3D)
App08:57![什么是定积分[高等数学24]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/5c8c71b363564ed2aa57b045bd5b14e2~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=%2Fdq0NaRvi4eahkxhYoWkyQfPC34%3D)
App21:43![积分中值定理[高等数学25]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/1f9e13e0921f4c03bf4bbe52c72ec65f~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=kCsdj2XZzwEo5y6MuaA3UJT2axY%3D)
App09:52
App17:38![定积分的换元法[高等数学26]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/98c772e478714761bfca2c4d1a97cfc7~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=N%2F6ZIK%2BJ8seGWepOvyCBeBUpeKs%3D)
App17:15![[高数下册1]向量的数量积，向量积，混合积](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/8fafc85116c643d18a12234272a6792a~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=TC1Dnkii8ZcA%2FCh46BAyEGyGU3A%3D)
App27:30![[高数下册2]空间中的平面方程和直线方程](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/641e4a6b0bc44a25a5da0481ec6c96d6~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=B9kqY810dkdqO2KhqwluhQqOGsw%3D)
App23:02![多元函数的极限与连续性[高数下册3]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/43b3473bad6449f2a2f177d94181ee75~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=T7apWMYu9xKBf2f%2FK17JUnpSgSc%3D)
App28:00![偏导数与高阶偏导数[高数下册4]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/cce162b9643d469e979ffcc8862ee3db~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=b7zEkbxh1sIt%2BVxR3YokDCZ74Ic%3D)
App21:47![多元函数的全微分[高数下册5]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/60639dde2fdb4ab298fc863b87ccd03d~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=va9jJHUGq9zwu0H75pFhBSvU02s%3D)
App25:42![多元复合函数求导法则[高数下册6]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/13b47be6747348bd9c3f3a8d3c0abf29~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=mo0u9magZTqC08paTtDsgO7HfEY%3D)
App22:45![多元函数隐函数求导法则与Jacobi行列式[高数下册7]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/bc62f6d364304761bfc983efb3b8a5df~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=BV48bo2d30z5XdKFgCC%2B955kli0%3D)
App19:18![方向导数与梯度[高数下册8]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/42dd554276584ebe95cf050b8b5d69cb~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=Xa3CKhwTGreAYEu0mRlDhl0VzNM%3D)
App17:25![二重积分的概念与性质[高数下册9]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/7920905eba7b41ff97ca8de77ac1721d~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=%2FdnDhVx8uq27RO5WIxipg5vEkVE%3D)
App17:03![二重积分计算法——直角坐标系计算法[高等数学10]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/0c14b406ffd641d384d4a75dff0fada6~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=nrHUBYIvWtUNeDf8M7ryKL7Up8c%3D)
App13:12![极坐标系中计算二重积分[高数下册11]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/e629fc11cfb24008b9dbe986d775348e~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=fyhkfsoehoZi8Ou7WZe9CjUhB2Q%3D)
App11:00![三重积分及其在平直系中的计算法[高数下册12]](http://p26-sign.bdxiguaimg.com/tos-cn-i-0004/b084b3d4355e4f89ae34a427317b6004~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=VnBSpnUVmjHIDsfJTregwAqbdJE%3D)
App14:47![[高等数学1.1]有界函数、无界函数，符号咋理解？](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/be2d1a15fd3c4609a8f89aab741b14d6~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=CZgn6go0Iq%2Bm30mM55xWKO9yBDU%3D)
App19:25![有理函数的不定积分[高等数学27]](http://p3-sign.bdxiguaimg.com/tos-cn-i-0004/60e3eb26b58b468580b712caf3fbd98b~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=20250121063818E884AE6A6BCA43B3FF8B&requestFrom=704&version_code=80402&x-expires=1768948699&x-signature=%2FUrg9ZwmI6KOD9hUMRDOAiWCr6U%3D)
App17:44
App15:13打开App观看
