Slope of a Tangent Line | Derivatives & Limits Explained – Calculus 12

Ever wondered what a derivative really means? This video from the MathSupport channel ( ⁨‪@mathsupportnow‬ ) offers a clear, visual explanation of the derivative as the slope of the tangent line, showing exactly how it's derived from the slope of a secant line using limits. Whether you’re just starting Calculus or reviewing core concepts, this video breaks down the first major idea in differential calculus in a way that’s easy to understand. In This Video, You’ll Learn: ✅ What is a tangent line and how it differs from a secant line ✅ How to use the limit process to find the slope of the tangent ✅ The limit definition of the derivative: f'(x) = lim(h→0) [f(x + h) - f(x)] / h ✅ The geometric meaning of a derivative ✅ How the secant line approaches the tangent as h → 0 ✅ Why this concept is foundational in all of calculus 00:00 – Introduction & Tangent Line Concept 00:52 – Secant Line & Point Q Setup 02:26 – Limit Process: Q Approaches P 03:18 – Formal Limit Definition of Slope 03:40 – Derivative Notation: 𝑓′(𝑎) 04:14 – Alternate Limit Form Using 𝑥 and 𝑎 05:21 – Application: Tangent Line Equation & Curve Analysis 05:34 – Wrap-Up & Encouragement Worked Example (For Viewers to Try): Let’s say: f(x) = x² . Using the limit definition: f'(x) = lim(h→0) [(x + h)² - x²] / h = lim(h→0) [x² + 2xh + h² - x²] / h = lim(h→0) [2xh + h²] / h = lim(h→0) 2x + h = 2x So the derivative of x² is 2x, which gives the slope of the tangent at any point x. 🎯 Who Is This Video For? ✔️ Grade 12 students in Canada and British Columbia (BC Calculus Curriculum) ✔️ First-year university or college students ✔️ Students studying AP Calculus AB, IB Math AA HL/SL, or A-Level Mathematics ✔️ Anyone starting their first calculus course globally ✔️ Teachers or tutors introducing derivatives visually 👍 Like if this lesson helped you 🔔 Subscribe for more step-by-step Math tutorials 💬 Comment on the video or suggest a future lesson that you like to see 📤 Share this with classmates, teachers and parents More Video lesson on Derivatives:    • Differentiation Rules Part II | Master the...   #TangentLine #DerivativeDefinition #Grade12Calculus #FinalExamReview #LimitsInCalculus #MathHelp #MathTutorial