Calculus 1 — 14.4: Chain Rule with Trig Functions скачать в хорошем качестве

Calculus 1 — 14.4: Chain Rule with Trig Functions

Learn the two-step method for differentiating trigonometric compositions: differentiate the outer trig function while leaving the inner function untouched, then multiply by the derivative of the inside as a separate factor. This video walks through derivatives of sin, cos, tan, csc, sec, and cot composed with inner functions, diagnosing the two most common chain rule mistakes students make. Key concepts covered: • The chain rule template for trig functions: d/dx[trig(g(x))] = trig'(g(x)) · g'(x) • The "two-beat rhythm" — outer derivative with inside unchanged, then multiply by the inside's derivative • Worked example: d/dx[cos(x⁴)] = -4x³ sin(x⁴) and why two common wrong answers arise • Error analysis: absorbing the chain factor into the trig argument vs. replacing the inside with its derivative • Derivatives of tan, csc, and cot compositions where the trig derivative itself has multiple factors • All six standard trig derivative formulas as a reference table • Practice problems: d/dx[sin(x³ + 1)] and d/dx[sec(5x)] • Three golden rules: leave the inside alone, multiply the chain factor outside, never place it inside the angle ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from    • Calculus 1 Lecture 2.6:  Discussion of the...