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Chain Rule with Trigonometry

Learn how to differentiate trigonometric functions easily with this straightforward guide. In just three simple steps, you’ll discover how to apply the generic derivative rules for sine, cosine, tangent, and their corresponding functions. Using the example of y = tan(6x² + 7x + 3), we’ll walk you through the process of finding the derivative step-by-step. By the end, you’ll be able to clean up your answer and understand how to tackle other trigonometric derivatives. Get ready to improve your calculus skills!

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Chain Rule with Trigonometry

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  1. Chain Rulewith Trigonometry Made By: Heather Hamm Class of 2010 In 3 Easy Steps!

  2. Generic Rule d/dx sin(something) = cos (something) d/dx (something) • y = sinu y’= cosu u’ • y= cosu y’= -sinu u’ • Y= tanu y’= sec²u u’ • Y= secu y’= secutanu u’ • Y= cscu y’= -cscucotu u’ • Y= cotu y’= -csc²u u’ argument

  3. Practice Equation: y= tan(6x² + 7x + 3) Remember: • Generic Rule: • Trigonometry (something) y= tan(6x² + 7x + 3) Something (AKA the argument) Trigonometry

  4. Step One The Derivative of Trigonometry with the argument • Original Equation: • y= tan(6x² + 7x + 3) • Derivative of tanu = sec²u u’ y= tan(6x² + 7x + 3) y’= sec² (6x² + 7x + 3)

  5. Step Two Step One answer with the Derivative of the argument at the end • After Step One: • y’ = sec² (6x² + 7x + 3) Applying Step Two: y’ = sec² (6x² + 7x + 3) (12x +7) Argument Derivative of Argument

  6. Step 3 Place the Derivative of the Argument at the beginning of the equation • Tidy Up the Answer Step Two Answer: y’ = sec² (6x² + 7x + 3) (12x + 7) Clean it up: y’ = (12x + 7) sec² (6x² + 7x + 3)

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