Chain Rule with Radicals: Why Rewriting as Exponents Changes Everything скачать в хорошем качестве

Chain Rule with Radicals: Why Rewriting as Exponents Changes Everything

Why fight the quotient rule when a simple rewrite gives you the same answer in four lines? This video shows how to convert radicals and fractions into exponent form before differentiating — turning messy chain rule problems into clean, systematic calculations. You'll work through two complete examples: differentiating √(5x²−1) and 1/(3x²+7)³, learning the general power rule workflow from rewrite to final answer. Along the way, we cover the two most common pitfalls — illegal cancellation through radicals and exponent subtraction errors — with concrete numeric checks that prove why the shortcuts don't work. Key concepts covered: • Rewriting radicals and reciprocals as power functions (√u = u^(1/2), 1/u² = u^(−2), etc.) • The general power rule as the chain rule applied to power functions • Step-by-step differentiation of √(5x²−1) using exponent rewrite • Why you cannot cancel terms through a radical or out of a binomial • Exponent subtraction with fractions and negatives (1/2 − 1 = −1/2, not 1/2) • Decision flowchart: when to use product rule, quotient rule, or negative exponent rewrite • Full worked example: differentiating 1/(3x²+7)³ in four lines • Matching your final answer's form to the original problem ───────────────────────────── ORIGINAL SOURCE ───────────────────────────── This video is based on content from:    • Calculus 1 Lecture 2.6:  Discussion of the...   All credit to the original creator for the source material. ───────────────────────────── About Ludium ───────────────────────────── Learn. Play. Discover. Ludium distills long lectures into focused concept videos so you can master one idea at a time. GitHub: https://github.com/Augustinus12835/au... #ChainRule #GeneralPowerRule #Calculus #Derivatives #NegativeExponents #Radicals #DifferentiationTechniques #MathEducation