Understanding the Chain Rule in Calculus for Trigonometric Functions
Explore the application of the chain rule in calculus to trigonometric functions. Learn how to differentiate functions involving sine, cosine, tangent, secant, and more using this fundamental rule. Master the techniques through visual examples and detailed explanations presented in this comprehensive guide.
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Presentation Transcript
Chapter 2.4: Chapter 2.4: The Chain Rule The Chain Rule HONORS CALCULUS/CALCULUS HONORS CALCULUS/CALCULUS
The Chain Rule ???(? ? ) = ? ? ? ? (?) ? = ??+ ? ? ? ? = ?? ????
? ??+ ?? ?(?) =
? ? ? = ?? ??
The Chain Rule and Product Rule ? ? = ??? ??
The Chain Rule and Quotient Rule ? ?? ? ??+ ? ? ? =
Alternate Method: Product Rule ? ?? ? ??+ ? ? ? =
Quotient Rule ? ? ? = ???+ ?
Product Rule ? ? ? = ???+ ?
Derivates of Trigonometric Functions dx dx d du d du = = sin cos cos sin u u u u dx dx d du d du = 2 tan sec = u u sec sec tan u u u dx dx dx dx d du d du = = 2 csc csc cot u u u cot csc u u dx dx dx dx
Applying the Chain Rule to Trigonometric Functions ? = ????? ? = ???(? ?) ? = ?????
Applying the Chain Rule to Trigonometric Functions ? = ??? ??? ? = ????(??)
Applying the Chain Rule to Trigonometric Functions ?(?) = ?????
