How to Find Tangent Lines Using Derivatives | Polynomials & Fractions скачать в хорошем качестве

How to Find Tangent Lines Using Derivatives | Polynomials & Fractions

Learn the step-by-step process for finding tangent lines using the derivative formula. This video walks through two complete examples—a polynomial (y = x²) and a rational function (y = 3/x)—showing you exactly how to handle the algebra that trips up most students. You'll master the key techniques: proper substitution of (x₀ + h) as a single input, resolving the 0/0 indeterminate form through factoring, and simplifying complex fractions with common denominators. 📚 KEY CONCEPTS COVERED: • The derivative formula m = lim(h→0) [f(x₀+h) - f(x₀)]/h for finding exact tangent slopes • Why (x₀ + h) must be substituted as ONE unified input—not separated • How the 0/0 indeterminate form signals you need to factor and cancel h • Polynomial technique: expansion and factoring (demonstrated with y = x²) • Rational function technique: common denominators and complex fraction simplification (demonstrated with y = 3/x) • Writing tangent line equations using point-slope form ━━━━━━━━━━━━━━━━━━━━━━━━ 📖 ORIGINAL SOURCE ━━━━━━━━━━━━━━━━━━━━━━━━ This video distills concepts from:    • Calculus 1 Lecture 1.5:  Slope of a Curve,...   Full credit to the original creator. Please visit the source for the complete lecture. ━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 ABOUT LECTURE DISTILLED ━━━━━━━━━━━━━━━━━━━━━━━━ Long lectures. Short videos. Core insights. We distill lengthy academic lectures into focused concept videos that respect your time while preserving the essential understanding. 🔗 GitHub: https://github.com/Augustinus12835/au... #Calculus #Derivatives #TangentLine #MathTutorial #CalculusHelp #LimitDefinition #DifferentialCalculus #MathEducation