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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.

EXAMPLE 1 Quotient Rule:

CONTINUED Applying the Quotient Rule: Combine like terms and simplify:

EXAMPLE 2 Rewrite: We know:

CONTINUED Applying the Quotient Rule: Simplifying:

CONTINUED

PRACTICE SAMPLE We know:

CONTINUED Applying the Quotient Rule: Simplifying:

CONTINUED

PRACTICE SAMPLE We begin by applying the Product Rule: 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:

CONTINUED We now apply the Quotient Rule for Combined result:

CONTINUED Simplify:

CONTINUED

QUESTIONS

Quotient Rules Links Quotient Rule Workshop Handout Product and Quotient Rules Handout Product Rule Workshop