Pre-Calc Homework Solutions 103

Pre-Calc Homework Solutions 103 - Section 3.7 x2 d 2 (x )...

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Unformatted text preview: Section 3.7 x2 d 2 (x ) dx x y 103 8. dy dx d dx (x 2 x x2 1)1/2 1 x x2 x2 (x 2 1)1/2 x x2 d dx x (x 2 1 d dx 1)1/2 12. x y d x y dx x y (x y) 1 dy dx 1 2 (x 2 1) 1/2 (2x) (x y)2 y) 1 dy dx 1 2x (x (x 2 1 x2 1)(x 2 1)1/2 x x dy dx y y dy dx x y)2 x dy dx y y dy dx 1 (x 2 1)3/2 2x 2y 2x dy dx (x (x 9. 2 1) 3/2 2x x 2y xy 2 6 d (6) dx (x x(x y)2 x dy dx dy dx y y y x y)2 dy dx d 2 (x y) dx d (xy 2) dx dy x(x x(x x y)2 y)2 y x x x y y x 2 dy dx y(2x) x(2y) x dx 2 dy dx y 2(1) 2xy dy dx dy x 2) dx dy dx 0 (2xy (2xy 2xy 2xy (x y)2 y 2) y 2) y2 x2 Alternate solution: x2 x 2(x x3 d 3 (x ) dx (2xy y) x 2y x x y y d (y) dx 10. d 3 (x ) dx x 3 y 3 18xy d (18xy) dx dy dx d 2 (x y) dx d (x) dx 3x 3y 2 d 3 (y ) dx 2 dy 3x 2 18y (1) 2 x2 dy dx 2 y(2x) 1) dy dx dy dx 1 1 1 dy dx 3y 2 dy dx 18x 18x) dx dy dx dy dx dy dx dy dx 18x 18y 18y 18y (x 3x 3x 2 3x x2 2 2xy 2xy 1 (3y 2 3x 2 3x 2 13. dy dx 3y 2 18x 6y x 2 y2 6x 11. y2 d 2 y dx dy dx dy dx dy dx 2y 2y x x d dx (x 1 1 x x 1 1 1)(1) (x d (1 x 1/2)1/2 dx 1 d (1 x 1/2) 1/2 (1 x 1/2) 2 dx 1 1 1/2 (1 x 1/2) 1/2 x 2 2 1 (1 x 1/2) 1/2x 1/2 4 d 3(2x 1/2 dx 14. (x 1)2 1)(1) dy dx 1) 1) 1) 1/3 (2x (2x x 15. dy dx 3/2 1/2 1/2 1/2 4/3 d dx 4/3 (2x 1/2 1) 2 1)2 1 y(x 1)2 (x ( x 4/3 3/2 ) (2x 1) d 3(csc x)3/2 dx 9 d (csc x)1/2 (csc x) 2 dx 9 (csc x)1/2( csc x cot x) 2 9 (csc x)3/2 cot x 2 ...
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