General Derivative Formulas & When Derivatives Don't Exist скачать в хорошем качестве

General Derivative Formulas & When Derivatives Don't Exist

📓 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) ───────────────────────────── ORIGINAL SOURCE ───────────────────────────── This video distills content from:    • Calculus 1 Lecture 1.5:  Slope of a Curve,...   Full credit to the original creator. Please visit and support the original 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 mathematics. Explore our resources: https://github.com/Augustinus12835/au... #Calculus #Derivatives #Mathematics #MathTutorial #CalculusTutorial #DerivativeFormula #LimitDefinition #MathEducation