Clever Clairaut Proof

In this video, I give a very clever proof of Clairaut's theorem, which says that if the partial derivatives f_xy and f_yx are continuous at a point, then must be equal. Usually this is proved using difference quotients, but here I give a proof using double integrals. I also give a nice proof using Green's theorem. This is a must-see video for multivariable calculus lovers! Clairaut Counterexample:    • Clairaut Counterexample   Fubini Counterexample:    • Fubini Counterexample   Green's Theorem:    • Green's Theorem   Multivariable Calculus Playlist:    • Multivariable Calculus   Partial Derivatives Playlist:    • Partial Derivatives   Subscribe to my channel:    / drpeyam   Check out my TikTok channel:   / drpeyam   Follow me on Instagram:   / peyamstagram   Follow me on Twitter:   / drpeyam   Teespring merch: https://teespring.com/stores/dr-peyam