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13112an3.9-11

# 13112an3.9-11 - c Kendra Kilmer February 3 2012 Section 3.4...

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c c Kendra Kilmer February 3, 2012 Section 3.4 - The Chain Rule The Chain Rule: If g is differentiable at x and f is differentiable at g ( x ) , then the composite function m ( x ) = f ( g ( x )) is differentiable at x and is given by In Leibniz notation, if y = f ( u ) and u = g ( x ) are both differentiable functions, then General Derivative Rules: If y = [ f ( x )] n then If y = sin [ f ( x )] then If y = e f ( x ) then If y = b f ( x ) then Example 1: Differentiate the following: a) f ( x ) = ( 4 x 2 + 7 x ) 5 b) g ( x ) = 6 ( x 1 / 2 3 x ) 4 c) y = 5 ( t 2 + 3 t + 4 ) 4 d) F ( x ) = e x 2 9

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c c Kendra Kilmer February 3, 2012 e) H ( x ) = 3 x 5 e x 4 f) h ( x ) = 3 4 ( 3 x + 2 ) 5 g) s ( t ) = p sin t + 1 5 + e t t 2 P 9 h) f ( x ) = ( 4 x 2 + 5 ) 6 ( 3 r ( 3 x 4 5 x + 7 ) 4 ) i) G ( x ) = 3 cos ( x 4 x ) 10
c c Kendra Kilmer February 3, 2012
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13112an3.9-11 - c Kendra Kilmer February 3 2012 Section 3.4...

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