Calculus 1 — 14.2: Product Rule with Chain Rule

Описание: 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

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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...