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Chain Rule with Trigonometry

Chain Rule with Trigonometry. Made By: Heather Hamm Class of 2010. In 3 Easy Steps!. Generic Rule. d/dx sin(something) = cos (something) d/dx (something). y = sinu y’= cosu u’ y= cosu y’= -sinu u’ Y= tanu y’= sec ² u u’ Y= secu y’= secutanu u’ Y= cscu y’= -cscucotu u’

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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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