Скачать или смотреть Derivative of a Function at a Point| Definition and Meaning in Calculus 1

📚 Derivative of a Function — Definition and Meaning
In this video, we’ll introduce the derivative of a function at a point, one of the most important concepts in calculus. You’ll learn how the derivative is defined using limits, what it represents, and how it connects to slopes and rates of change.

🔍 What You’ll Learn in This Video:
✅ Limit Definitions of the Derivative
✔ f′(a) = lim (h → 0) [(f(a + h) − f(a)) / h]
✔ f′(a) = lim (x → a) [(f(x) − f(a)) / (x − a)]

✅ Interpretation of the Derivative
✔ Instantaneous rate of change at a point
✔ The slope of the tangent line to the graph of f(x) at x = a

✅ Visual Understanding
✔ How the tangent line relates to secant lines as h → 0
✔ Graphical representation of Δx, Δf, and the tangent slope

By the end of this video, you’ll understand the definition of the derivative, how it is formed from limits, and why it is the foundation of differential calculus.

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Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

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