The Total Differential & Tangent Plane Explained Visually

In the last video, we formalized partial derivatives. But what happens when both x and y change simultaneously? To answer this, we combine our partial derivatives into a single, powerful tool: the total differential. In this video, we explore the geometric meaning of differentials and how they lead directly to the equation of the tangent plane. We will see how the flat tangent plane provides the best linear approximation of a curved surface, and work through a complete step-by-step example using a paraboloid. Inspired by the rigorous yet visual approach to multivariable calculus, this video bridges the gap between partial derivatives and the true definition of differentiability. All animations created programmatically with Python and Manim. Watch the full Calculus 2 Playlist:    • Visualizing Multivariable Functions: The P...   #TotalDifferential #TangentPlane #Calculus2 #MultivariableCalculus #MathVisualization #Manim #LinearApproximation #MathExplained