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Understanding the Product and Quotient Rules for Derivatives in AP Calculus

This lesson covers the Product and Quotient Rules for derivatives, essential concepts in AP Calculus. The Product Rule states how to differentiate the product of two functions, while the Quotient Rule applies when dividing two functions. Through examples, you will learn to successfully apply these rules to find derivatives. Practice problems will enhance your understanding, including a specific example involving differentiable functions at a point. Ensure your algebra is accurate to avoid mistakes while applying these rules.

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Understanding the Product and Quotient Rules for Derivatives in AP Calculus

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  1. AP CALCULUS 1009 : Product and Quotient Rules

  2. PRODUCT RULE FOR DERIVATIVES  Product Rule: (In Words) ________________________________________________

  3. PRODUCT RULE FOR DERIVATIVES EX:

  4. Example Using the Product Rule GRADING:

  5. PRODUCT RULE FOR DERIVATIVES EX: Given u and v are differentiable at x = 2 and u(2) = 3 u’(2) = 4 v(2) = - 2 v’(2) = 5

  6. QUOTIENT RULES FOR DERIVATIVES If you can reduce the fraction - - - - - DO

  7. QUOTIENT RULES FOR DERIVATIVES Quotient Rule: (In Words) _______________________________________________ ¡ ¡ ¡ ¡ WATCH YOUR ALGEBRA ! ! ! !

  8. QUOTIENT RULES FOR DERIVATIVES EX:

  9. Example Using the Quotient Rule GRADING:

  10. QUOTIENT RULES FOR DERIVATIVES EX:

  11. QUOTIENT RULE FOR DERIVATIVES EX: Given u and v are differentiable at x = 2 and u(2) = 3 u’(2) = 4 v(2) = - 2 v’(2) = 5

  12. Last Update • 9/17/10 Assignment: p 124 # 15 - 35 odd omit 19

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