Calculus 1 — 14.2: Product Rule with Chain Rule скачать в хорошем качестве

Calculus 1 — 14.2: Product Rule with Chain Rule

Description When an expression requires both the product rule and the chain rule, which do you apply first? This video teaches a reliable diagnostic: identify the outermost operation, apply that rule first, then work inward layer by layer. We walk through the complete differentiation and simplification of x²·(x²−5)^(1/3), including factoring the result into a clean, usable form and applying it to find a tangent line equation. Key concepts covered: • The "outermost operation" diagnostic for choosing between product, quotient, and power rules • Applying the product rule as the first step when two functions are multiplied • Using the general power rule (chain rule for powers) on sub-expressions generated by the product rule • Why forgetting the derivative of the inner function invalidates the entire answer • Factoring fractional exponents by pulling out the lowest power of the common base • Combining terms over a common denominator to reach a simplified derivative • Using the simplified derivative to compute a tangent line via point-slope form • Common mistakes: distributing exponents into parentheses, omitting the chain rule factor, and misidentifying the outermost operation — ORIGINAL SOURCE This video is based on content from the following source. Full credit to the original creator:    • Calculus 1 Lecture 2.6:  Discussion of the...