The Power Rule for Derivatives Explained (From First Principles) скачать в хорошем качестве

The Power Rule for Derivatives Explained (From First Principles)

Ever wondered why the power rule works? In this video, we derive it from scratch using the limit definition, then show you how to apply it instantly to any power function. You'll understand not just HOW to use d/dx[xⁿ] = nxⁿ⁻¹, but WHY it works—building mathematical intuition that sticks. 📚 Key concepts covered: • Why the derivative of any constant equals zero (horizontal lines have no slope) • Step-by-step derivation of the power rule using first principles and limits • The power rule formula: bring down the exponent, subtract one from the power • Practice examples from simple (x²) to complex (s¹⁵) • Edge case: why d/dx[x] = 1 connects calculus back to basic algebra ⏱️ Timestamps: 0:00 - The shortcut that replaces pages of algebra 0:30 - Derivatives of constants 1:15 - Deriving the power rule from the limit definition 3:00 - The general power rule formula 3:30 - Practice examples 4:30 - The special case of d/dx[x] = 1 5:00 - Rapid-fire practice & real-world applications ━━━━━━━━━━━━━━━━━━━━━━━━ 📖 ORIGINAL SOURCE ━━━━━━━━━━━━━━━━━━━━━━━━ This video distills concepts from:    • Calculus 1 Lecture 2.2:  Techniques of Dif...   Full credit to the original creator. Please visit the source for the complete lecture. ━━━━━━━━━━━━━━━━━━━━━━━━ 🎓 About Lecture Distilled ━━━━━━━━━━━━━━━━━━━━━━━━ Long lectures. Short videos. Core insights. We transform lengthy educational content into focused, digestible concept videos—helping you learn faster without losing depth. 🔗 GitHub: https://github.com/Augustinus12835/au... #calculus #derivatives #powerrule #mathematics #mathhelp #calculustutorial #learnmath #firstprinciples