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Chap3_Sec4

# Chap3_Sec4 - CHAIN RULE Differentiate y = x 3 – 1 100...

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It seems plausible if we interpret derivatives as rates of change. Regard: square4 du / dx as the rate of change of u with respect to x square4 dy / du as the rate of change of y with respect to u square4 dy / dx as the rate of change of y with respect to x If u changes twice as fast as x and y changes three times as fast as u , it seems reasonable that y changes six times as fast as x . So, we expect that: CHAIN RULE dy dy du dx du dx =

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Find F’ ( x ) if 2 ( ) 1 F x x = + Example 1 (3.4) CHAIN RULE
Differentiate: a. y = sin( x 2 ) b. y = sin 2 x Example 2 (3.4)

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Unformatted text preview: CHAIN RULE Differentiate y = ( x 3 – 1) 100 Example 4 (3.4) : Find f’ ( x ) if Example 3 (3.4) POWER RULE WITH CHAIN RULE 3 2 1 . ( ) 1 f x x x = + + Find the derivative of Example 6 (3.4) : Differentiate y = (2 x + 1) 5 ( x 3 – x + 1) 4 9 2 ( ) 2 1 t g t t- = + Example 5 (3.4) POWER RULE WITH CHAIN RULE Differentiate y = e sin x Example 9 (3.4): Differentiate y = e sec 3 θ Example 7 (3.4) CHAIN RULE...
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