How to Find Tangent Lines Using Derivatives | Polynomials & Fractions

Описание: 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

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📖 ORIGINAL SOURCE
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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.

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🎓 ABOUT LECTURE DISTILLED
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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...

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