243_James Stewart Calculus 5 Edition Answers

243_James Stewart Calculus 5 Edition Answers - Stewart...

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Unformatted text preview: Stewart Calculus ET 5e 0534393217;3. Differentiation Rules; 3.5 The Chain Rule 1 f (t )= (1+tan t ) 3 1/3 3 / f (t )= 1+tan t =(1+tan t ) 3 3 / 13. y=cos (a +x ) 3 3 mx 3 2 2 sec t 2 sec t = 3 2 3 (1+tan t ) 3 2 3 3 y = sin (a +x ) 3x [ a is just a constant] = 3x sin (a +x ) / 14. y=a +cos x 15. y=e 3 2/3 2 3 2 y =3(cos x) ( sin x) [ a is just a constant] = 3sin xcos x / d ( mx)=e dx mx y =e mx mx ( m)= me / 16. y=4sec 5x y =4sec 5xtan 5x(5)=20sec 5xtan 5x 5 28 17. g(x)=(1+4x) (3+x x ) / 5 27 28 4 g (x) =(1+4x) 8(3+x x ) (1 2x)+(3+x x ) 5(1+4x) 4 4 27 2 4 27 2 4 27 2 =4(1+4x) (3+x x ) [2(1+4x)(1 2x)+5(3+x x )] 2 =4(1+4x) (3+x x ) [(2+4x 16x )+(15+5x 5x )] =4(1+4x) (3+x x ) (17+9x 21x ) 4 33 4 18. h(t )=(t 1) (t +1) / 4 3 3 3 2 3 4 4 2 3 h (t ) =(t 1) 4(t +1) (3t )+(t +1) 3(t 1) (4t ) 24 23 3 4 3 24 23 3 4 =12t (t 1) (t +1) [(t 1)+t (t +1)]=12t (t 1) (t +1) (2t +t 1) 4 2 3 19. y=(2x 5) (8x 5) / 3 2 3 4 2 4 y =4(2x 5) (2) (8x 5) +(2x 5) ( 3) (8x 5) (16x) 3 2 =8(2x 5) (8x 5) 2 2 3 1/3 / 20. y=(x +1) (x +2) 2 21. y=xe x / 4 2 4 1/3 2 48x(2x 5) (8x 5) 2 y =2x (x +2) +(x +1) 2 x y =xe ( 2x)+e 2 x 2 1= e x 2 1 3 ( 2x +1)=e 2 (x +2) 2/3 2 1/3 (2x)=2x (x +2) 2 1+ x +1 2 3 (x +2) 2 x 2 (1 2x ) 2 ...
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This note was uploaded on 08/02/2011 for the course MATH 1B taught by Professor Reshetiken during the Spring '08 term at University of California, Berkeley.

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