Chain Rule - pp

Chain Rule - pp - (8<<<Press any Key to...

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The Chain Rule The chain rule involves “taking the derivative normally” (often with the use of the power rule THEN taking the derivative of “what’s inside”). Consider a basi example…. f x ( 29 = 3 x 2 - 5 ( 29 3 Think of this like it ' s f ( x ) = z 3 and z = 3 x 2 - 5 f '( x ) = 3 z 2 d dx z So, use your basic power rule…. f ' x ( 29 = 3 x 2 - 5 ( 29 3 2 2 3 2 Now take the derivative of “what’s inside” and ‘tack that on the end’. f ' x ( 29 = 3 3 x 2 - 5 ( 29 2 6x <<<Press any Key to Continue>>> Simplifying give us the final result…. . f '( x ) = 18 x 3 x 2 - 5 ( 29 2
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Let’s do another example…. f x ( 29 = ln 8 x - 5 ( 29 Think of this like it ' s f ( x ) = ln( z ) and z = 8 x - 5 f '( x ) = 1 z d dx z So, take the derivative of the “log”…. f ' x ( 29 = 1 8 x - 5 ( 29 Now take the derivative of “what’s inside” and ‘tack that on the end’.
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Unformatted text preview: (8) <<<Press any Key to Continue>>> f ' x ( 29 = 1 8 x-5 ( 29 Simplifying give us the final result…. . f '( x ) = 8 8 x-5 Let’s do one final example…. f x ( 29 = e 3 x 4 Think of this like it ' s f ( x ) = e z and z = 3 x 4 ⇒ f '( x ) = e 3 x 4 d dx z f ' x ( 29 = e 3 x 4 Now take the derivative of “what’s inside” and ‘tack that on the end’. <<<Press any Key to Continue>>> First takethederivativeof the " e z " part f ' x ( 29 = e 3 x 4 12 x 3 ( 29 or f ' x ( 29 = 12 x 3 e 3 x 4...
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This note was uploaded on 06/15/2011 for the course MATH 122 taught by Professor Kustin during the Spring '08 term at South Carolina.

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Chain Rule - pp - (8<<<Press any Key to...

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