# hw3-12 - c 4 x 3 f x 4 f ′ g ′ d 4 x 3 fg x 4 f ′ g...

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Homework 3/12 Throughout this homework, f , g and h are functions of x . In all problems, Fnd dy/dx . 1. (a) y = x 4 (b) y = f 4 (c) y = f ( x 4 ) 2. (a) y = tan x (b) y = tan( f ( x )) (c) y = f (tan x ) 3. (a) y = x 4 (sin x + cos x ) (b) y = x 4 ( f + g ) (c) y = x 4 f + g (d) y = x 4 fg (e) y = x 4 fg 4. (a) y = f 4 g 3 (b) y = f 2 - g 2 h (c) y = x 2 f ( x 2 ) 5. Section 3.5: 73, 75. 6. Section 3.2: 47. Answers 1. a) 4 x 3 ; b) 4 f 3 f ; c) 4 x 3 f ( x 4 ). 2. a) sec 2 x ; b) sec 2 ( f ( x )) f ( x ); c) f (tan x ) sec 2 x . 3. a) 4 x 3 (sin x + cos x ) + x 4 (cos x - sin x ); b) 4 x 3 ( f + g ) + x 4 ( f + g
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Unformatted text preview: ); c) 4 x 3 f + x 4 f ′ + g ′ ; d) 4 x 3 fg + x 4 ( f ′ g + fg ′ ); e) 4 x 3 fg-x 4 ( f ′ g + fg ′ ) ( fg ) 2 . 4. a) 4 f 3 f ′ g 3 + 3 g 2 g ′ f 4 ; b) (2 ff ′-2 gg ′ ) h-( f 2-g 2 ) h ′ h 2 ; c) 2 xf ( x 2 ) + 2 x 3 f ′ ( x 2 ). 1...
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