a f x x 3 2 x 2 3 x 4 1 b g s s 1 7 s 2 7 s 3 7 s 4 7 Exercise 4 4 88 In the

# A f x x 3 2 x 2 3 x 4 1 b g s s 1 7 s 2 7 s 3 7 s 4 7

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( a ) f ( x ) = - x 3 + 2 x 2 + 3 x 4 + 1 ; ( b ) g ( s ) = s 1 7 - s 2 7 s 3 7 + s 4 7 . Exercise 4 . 4 : 88 In the following problem, assume that f ( x ) and g ( x ) are differentiable at x . Find an expression for the derivative of y in terms of f ( x ) , g ( x ) , f 0 ( x ) and g 0 ( x ). y = 2 f ( x ) + x 3 g ( x ) . For Section 4 . 5 Exercise 4 . 5 : 810 , 12 In the following problems, differentiate the functions with respect to the independent variable. ( a ) f ( x ) = p 5 x + 3 x 4 ; ( b ) f ( x ) = 2 (1 - 2 x 2 ) 3 ; ( c ) f ( x ) (1 - 3 x 2 ) 3 (3 - x 2 ) 2 . Exercise 4 . 5 : 40 , 42 , 46 In the following problems, find dy dx by applying the chain rule repeatedly. ( a ) y = ( p 1 - 2 x 2 + 1) 2 ; ( b ) y = (1 + 2( x + 3) 4 ) 2 ; y = (2 x + 1) 2 - x (3 x 3 + 1) 3 - x 2 2
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