Calc 2.3a

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2.3A PRODUCT AND QUOTIENT RULE Goals: To differentiate a product To differentiate a quotient To find derivative of tangent, cotangent, secant and cosecant To find higher-order derivatives

[object Object],[object Object],[object Object],[object Object],This rule can be extended to three products or more, see page 119 at the bottom of the page!

EXAMPLE 1, P. 120 USING THE PRODUCT RULE ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],Putting in factored form as much as possible allows us to find the places where a horizontal tangent occurs more easily (where y’ = 0)

[object Object],[object Object],[object Object],[object Object],Use the product rule if __________________________. Use Constant rule if ____________________________. both factors are variable one of the factors is constant.

Break out that cowboy accent! Low dehigh – high delow all over low squared! http://www.youtube.com/watch?v=DdV2UZV7AoA

[object Object],[object Object],In general, see if numerator factors, and keep denominator in a factored form Note liberal use of parentheses!

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

CAUTION: NOT EVERY QUOTIENT DESERVES THE QUOTIENT RULE!!!! ,[object Object]

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Calc 2.3a

1. 2.3A PRODUCT AND QUOTIENT RULE Goals: To differentiate a product To differentiate a quotient To find derivative of tangent, cotangent, secant and cosecant To find higher-order derivatives

6. Break out that cowboy accent! Low dehigh – high delow all over low squared! http://www.youtube.com/watch?v=DdV2UZV7AoA

10.

11.

Calc 2.3a

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