Implicit Differentiation Explained: Horizontal & Vertical Tangent Lines | AP Calculus AB

In this video, I'm walking through implicit differentiation and how we can use it to find horizontal and vertical tangent lines. We start by talking about when and why we need implicit differentiation, especially when solving for y gives us multiple functions instead of one. I also explain how derivatives relate to tangent lines, why tangent lines represent instantaneous rates of change, and how they're different from secant lines. Then we work through implicit differentiation step by step before using our derivative to find horizontal and vertical tangent lines. We'll cover: Recognizing when implicit differentiation is needed Finding derivatives without isolating y Understanding tangent lines versus secant lines Finding horizontal tangent lines by setting the derivative equal to zero Finding vertical tangent lines when the derivative is undefined Writing the actual equations of those tangent lines My goal isn't for you to memorize a bunch of rules and hope you remember which one to use on a test. I want you to understand what you're doing, why you're doing it, and how to recognize what a problem is asking you to find. Rigor without shame. Mistakes are information. https://patchmath.com #APCalculusAB #APCalculus #ImplicitDifferentiation #TangentLines #HorizontalTangents #VerticalTangents #Derivatives #Calculus #PatchMath