Question: a. f ( x ) = 3 x 4 ( 1 2 x ) 7 f(x)=3x 4 (12x) 7 Use the product rule and chain

a. f ( x ) = 3 x 4 ( 1 2 x ) 7 f(x)=3x 4 (12x) 7 Use the product rule and chain rule: f ( x ) = d d x ( 3 x 4 ) ( 1 2 x ) 7 + 3 x 4 d d x ( ( 1 2 x ) 7 ) f (x)= dx d (3x 4 )(12x) 7 +3x 4 dx d ((12x) 7 ) = 12 x 3 ( 1 2 x ) 7 + 3 x 4 7 ( 1 2 x ) 6 ( 2 ) =12x 3 (12x) 7 +3x 4 7(12x) 6 (2) = 12 x 3 ( 1 2 x ) 7 42 x 4 ( 1 2 x ) 6 =12x 3 (12x) 7 42x 4 (12x) 6

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