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**Unformatted text preview: **3.6 The Chain Rule Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 U.S.S. Alabama Mobile, Alabama We now have a pretty good list of “shortcuts” to find derivatives of simple functions. Of course, many of the functions that we will encounter are not so simple. What is needed is a way to combine derivative rules to evaluate more complicated functions. → Consider a simple composite function: 6 10 y x =- ( 29 2 3 5 y x =- If 3 5 u x =- then 2 y u = 6 10 y x =- 2 y u = 3 5 u x =- 6 dy dx = 2 dy du = 3 du dx = dy dy du dx du dx = ⋅ 6 2 3 = ⋅ → and another: 5 2 y u =- where 3 u t = ( 29 then 5 3 2 y t =- 3 u t = 15 dy dt = 5 dy du = 3 du dt = dy dy du dt du dt = ⋅ 15 5 3 = ⋅ ( 29 5 3 2 y t =- 15 2 y t =- 5 2 y u =- → and one more: 2 9 6 1 y x x = + + ( 29 2 3 1 y x = + If 3 1 u x = + 3 1 u x = + 18 6 dy x dx = + 2 dy u du = 3 du dx = dy dy du dx du dx = ⋅ 2 y...

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