Calculus 1 — 11.2: Product Rule Worked Examples скачать в хорошем качестве

Calculus 1 — 11.2: Product Rule Worked Examples

Three worked examples show why the product rule matters — starting with a polynomial product you can verify by expanding, moving to radicals with fractional exponents, and ending with a function you have no formula for. That final case, where only a point value and derivative are given, reveals the real power of the product rule. Key concepts covered: • The product rule formula: d/dx[f(x)·g(x)] = f'(x)·g(x) + f(x)·g'(x) • Verifying the product rule by distributing (x²−1)(3x⁴+2x) and differentiating term by term • Why the derivative of a product is NOT the product of the derivatives • Converting radicals to fractional exponents: √x = x^(1/2), ∛x = x^(1/3), 1/√x = x^(−1/2) • Applying the power rule to fractional exponents and careful exponent arithmetic • Differentiating (1+x²)·√x using the product rule, with verification • Using the product rule with unknown functions: finding G'(2) when G(x) = (x²+1)·f(x) given only f(2) = 3 and f'(2) = −1 • The product rule spectrum: optional (poly × poly), recommended (poly × radical), required (known × unknown) ORIGINAL SOURCE This video distills content from the following source:    • Calculus 1 Lecture 2.3:   The Product and ...   All credit for the original educational content belongs to the original creator.