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In Exercises 1-10, find the differential dy in each of the given functions. Simplify all answers. BOX your final answer. 1. y=5x -2x3 +3x-1 2. y= (2x] - 3x +13x -2) 2x - 3 3. y= 3x + 4 4. xy+xy' -y'+x' =2 5. y = In(3x] + 5x +4)' 6. y = sin(3x+2) 7. y = Arcsin 8. yzxel 9. V=ethx 10. y = (sin.x) In Exercises 11 - 20, find the equation of the tangent and normal lines as indicated. Box your final answer. 11. Find the equations of the tangent and normal lines to the curvey = x2 - 6x + 4 at the point (2, - 4). 12. Find the equations of the tangent and normal lines to the curve 2x3 + 2y' - 9xy = 0 at the point (1, 2). 13. Find the equations of the tangent lines to the cubic y = x3 - 2x + 3 parallel to the line 10x - y = 3. 14. Find the equations of the tangent lines to the curve y = x* - 6x perpendicular to the line x - 2y + 6 = 0. 15. Find the equations of the tangent and normal lines to the curve y = sin 3x at x = = 16. Find the equations of the tangent and normal lines to the curve 16x* + y* = 32 at its points of intersection with the line y = 2. 17. Find the equations of the normal line to the curve x2 + xy + y? - 3y = 10 at the point (2, 3). 18. Find the equations of the normal lines to the curve y = x - 4x that is parallel to the line x + 8y = 8. 19. Locate the points on the curve y = 2_2 where the tangents lines parallel to the x-axis. 20. Locate the points on the curve xy = (1 - x - y) where the tangents lines parallel to the x- axis. In Exercises 21 - 30, find - . Use the given relation in its implicit form. Simplify all answers. Box your final answer. 21. x3 + y3 - 4xy = 0 22. x2 + xy2 + y2 =5 23. xy - Vxty = 4 24. (x+ y)3 = (x-y)2 25. x2 - 4 xy + y? = x 26. ylnx - xlny = c 27. arcsin = + arccos= = 1 28. In(x2 + y2) + 2 arctan = 1 29. yln(x2 + y?) = x+ c 30. 4 In(secy + tany) - 2x - sin 2x = c