Chain Rule with Trig Functions: The Two-Beat Rhythm That Prevents Every Common Mistake скачать в хорошем качестве

Chain Rule with Trig Functions: The Two-Beat Rhythm That Prevents Every Common Mistake

Three students differentiate cos(x⁴) and get three different answers — but only one is correct. This video breaks down exactly how the chain rule works with all six trigonometric functions, identifies the two most common errors students make, and gives you a reliable two-step method that works every time: differentiate the trig function with the inside untouched, then multiply by the derivative of the inside as a separate factor. Key concepts covered: • The chain rule applied to trigonometric compositions: f(g(x)) → f'(g(x)) · g'(x) • Worked examples with cos(x⁴), sin(4x⁵), tan(3x²−2x), csc(x³), and cot(x²) • The two most common chain rule errors: multiplying the chain factor into the trig argument, and replacing the inner function with its derivative • Complete reference table for all six trig derivatives (sin, cos, tan, csc, sec, cot) • Why co-functions (cosine, cosecant, cotangent) always carry a negative sign • Practice problems: d/dx[sin(x³+1)] and d/dx[sec(5x)] • Three golden rules for chain rule with trig functions ───────────────────────────── ORIGINAL SOURCE ───────────────────────────── This video is based on content from:    • Calculus 1 Lecture 2.6:  Discussion of the...   All credit for the original educational content belongs to the original creator. ───────────────────────────── 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 #TrigDerivatives #Calculus #Differentiation #TrigFunctions #MathEducation #AP_Calculus #DerivativeRules