Calculus 1 — 13.2: Six Trigonometric Derivatives

Описание: You don't need to memorize all six trigonometric derivatives separately. If you know that the derivative of sine is cosine and the derivative of cosine is negative sine, the quotient rule and the Pythagorean identity generate the other four. This video builds every trig derivative from scratch and reveals the structural patterns — the co-function rule, the sign pattern, and the period-four derivative cycle — that replace brute memorization with understanding.

Key concepts covered:
• The two foundation derivatives: d/dx(sin x) = cos x and d/dx(cos x) = −sin x
• Deriving d/dx(tan x) = sec²x using the quotient rule and the Pythagorean identity
• Deriving d/dx(sec x) = sec x · tan x by factoring sin x / cos²x
• The "co- means negative" pattern: cosine, cotangent, and cosecant derivatives all carry a negative sign
• Mirror structure across pairs: swap to co-functions and add a negative to get the paired derivative
• The period-four derivative cycle of sine and cosine
• Using modular arithmetic (remainder after dividing by 4) to find the nth derivative of sin x or cos x
• Worked examples: the 99th derivative of sin x and the 6th derivative of sin x

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ORIGINAL SOURCE
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This video distills concepts from the following source:
   • Calculus 1 Lecture 2.5:   Finding Derivati...  
All credit for the original educational content belongs to the original creator.