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Calculus
6. Derivatives of Special Functions
6.1 Derivative of trigonometric functions
Derivative of trigonometric functions
What You'll Learn
Memorize the six derivatives of trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant)
Recognize that derivatives of all co-functions (cosine, cotangent, cosecant) are negative
Apply the chain rule to trigonometric functions using the bracket technique
Differentiate composite trigonometric functions with nested trig and power functions
Combine power rule and trig derivatives when dealing with expressions like sin(x) vs sin(x)
What You'll Practice
1
Finding derivatives of sine and cosine functions with polynomial arguments
2
Differentiating expressions with exponents applied to trig functions vs. their arguments
3
Taking derivatives of nested trigonometric functions like sin(cos(tan(x)))
4
Using the bracket technique to simplify chain rule applications
Why This Matters
Mastering trigonometric derivatives is essential for calculus success, as these functions appear everywhere in physics, engineering, and higher mathematics. The chain rule with trig functions unlocks your ability to handle complex real-world models involving waves, oscillations, and periodic behavior.
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Trigonometric Derivatives
Chain Rule
Power Rule
Composite Functions
Bracket Technique
Co-functions
Calculus
RI Curriculum Aligned