Multivariable Calculus 27 | Application of the Implicit Function Theorem [dark version]

📝 Find more here: https://tbsom.de/s/mc 👍 Support the channel on Steady: https://steadyhq.com/en/brightsideofm... Other possibilities here: https://tbsom.de/sp You can also support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmath... Or via Patreon:   / bsom   Or via other methods: https://thebrightsideofmathematics.co... Join this channel on YouTube:    / @brightsideofmaths   💬 Access to the community forum: https://thebrightsideofmathematics.co... 🕚 Early access for videos: https://thebrightsideofmathematics.co... ❓ FAQ: https://thebrightsideofmathematics.co... 🛠️ What tools do you use: https://thebrightsideofmathematics.co... Please consider to support me if this video was helpful such that I can continue to produce them :) Each supporter gets access to the additional material. If you need more information, just send me an email: https://tbsom.de/s/mail Watch the whole video series about Multivariable Calculus and download PDF versions, quizzes and exercises: https://tbsom.de/s/mc Supporting me via Steady is the best option for me and you. Please consider choosing a supporter package here: https://tbsom.de/s/subscribe 🌙 There is also a dark mode version of this video:    • Multivariable Calculus 27 | Application of...   🔆 There is also a bright mode version of this video:    • Multivariable Calculus 27 | Application of...   🔆 To find the YouTube-Playlist, click here for the bright version:    • Multivariable Calculus   🌙 And click here for the dark version of the playlist:    • Multivariable Calculus [dark version]   🙏 Thanks to all supporters! They are mentioned in the credits of the video :) This is my video series about Multivariable Calculus also known as Analysis with more variables or in higher dimensions. I hope that it will help everyone who wants to learn about it. We discuss partial derivatives, the nabla operator, gradient, Jacobians, Hessian, Lagrange multipliers, extrema, Lagrange function, and so on. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community 00:00 Introduction 00:00 Inverse Function Theorem 01:52 Implicit Function Theorem 01:52 Implicit Function Theorem 02:07 Correction: there is no connection between the two differently coloured $k$s. It would have been better to use two different symbols there. 02:56 Application of the Implicit Function Theorem for polynomials 06:09 General case of an arbitrary polynomial 09:55 Outro #MultivariableCalculus #Analysis #Integral #Calculus #Derivatives #Mathematicspdt #Lagrange (This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on) For questions, you can contact me: https://steadyhq.com/en/backend/messa... The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start