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Slide 2 The Quotient Rule Brought To You By Tutorial Services The Math Center Slide 3 The Quotient Rule The Quotient Rule is used when there are two or more functions being divided. The derivative of (f(x)/g(x)) is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. The order in which you derive when using the Quotient Rule is very important, you must derive in the exact order the rule says to, otherwise the result will not be right. Slide 4 EXAMPLE 1 Quotient Rule: Slide 5 CONTINUED Applying the Quotient Rule: Combine like terms and simplify: Slide 6 EXAMPLE 2 Rewrite: We know: Slide 7 CONTINUED Applying the Quotient Rule: Simplifying: Slide 8 CONTINUED Slide 9 PRACTICE SAMPLE We know: Slide 10 Applying the Quotient Rule: CONTINUED Simplifying: Slide 11 CONTINUED Slide 12 PRACTICE SAMPLE From the equation, we can see that there are two functions being multiplied, while two are being divided, so we can use the Product Rule in combination with the Quotient Rule to solve the problem. We begin by applying the Product Rule: Slide 13 CONTINUED We now apply the Quotient Rule for Combined result: Slide 14 CONTINUED Simplify: Slide 15 CONTINUED Slide 16 QUESTIONS Slide 17 Quotient Rules Links Quotient Rule Workshop Handout Quotient Rule Workshop Handout Quotient Rule Workshop Handout Quotient Rule Workshop Handout Product and Quotient Rules Handout Product and Quotient Rules Handout Product and Quotient Rules Handout Product and Quotient Rules Handout Product Rule Workshop Product Rule Workshop Product Rule Workshop Product Rule Workshop