General Derivative Formulas & When Derivatives Don't Exist

Описание: 📓 Interactive Notebook: https://ludium.ai/courses/calculus-1/...

Why calculate the slope at every single point when you could have one formula that works everywhere? In this video, you'll learn how to derive a general derivative formula that gives you the slope at ANY point on a curve—just plug in your x-value. We'll also explore the critical cases where derivatives break down completely.

Key concepts covered:
• Deriving a general derivative formula instead of calculating slopes one point at a time
• The conjugate multiplication technique for handling radical functions like √x
• Why derivatives fail at discontinuities (gaps in functions)
• Why derivatives don't exist at sharp corners/cusps (absolute value at x=0)
• The unifying concept: slope, instantaneous velocity, and rate of change are mathematically identical

Worked example: Full step-by-step derivation of the derivative of √x, resulting in the formula 1/(2√x)

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ORIGINAL SOURCE
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This video distills content from:
   • Calculus 1 Lecture 1.5:  Slope of a Curve,...  

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