. o - . oay For Exercises | - 5, use implicit differentiation to find , ar Ix 1. x*+3y2=37 i 2. 3\\&4=e'+; 3. +zln(_v)=%x"'.' 1,7 and 1 1 4. 3:+2(@")-10x = \\'F - 5. 0.1y ~In(x) = 7log,(y) + 7 For Exercises 6 - 8, use implicit differentiation to find the slope of the line tangent to the graph of the equation at the given point. 6. In(y)+9 = %r' at(3,1) 1 7. -6 + Z_\\"" 2In(x) = -8 at (,0) 8. 19-3x>+9" =4/y at (0,25) For Exercises 9 - 11, use implicit differentiation to find the equation of the line tangent to the graph of the equation at the given point, 9. 7y*e* -2y =103 at (0,4) 10. 0.4/ +3.6 =In(y)+2x" at (2,1) 11. -3x+5 =-4y* - 17 at (6,0) For Exercises 12 - 14, suppose x and y are functions of and are related by the given equation. Use the information to find dt dx 12. y=4x>-5x+3, =2,and x= -6 dr 15, No Spots Left sells dishwashers and has a weekly cost equation given by C = 3500+ 14x+0.2x%, where C is the cost, in dollars, when x dishwashers are sold each week. If the number of dishwashers the company sells is increasing at a rate of 65 dishwashers per week, find the rate at which the company's cost is changing with dC dx respect to time when 250 dishwashers are sold each week. In other words, find i if we know & =65 t t dishwashers per week and x = 250 dishwashers. . The monthly profit equation for a company that c,el]q dEQigner handbags is given by P =-0.2x% +430x 00{] where P ist rs, when x han ags are sold each month. If the number of hang@ba ncrea@ing rat per month, find the rate at which the com n h res ct tim gs are sold each month. In other words, find E if we know _.' 135 handbags per month and x = 80! handbag% . Glow Kicks, a company that sells glow in the dark sneakers, has a weekly revenue equation given by R =207x-0.2x2, where R is the revenue, in dollars, from selling x pairs of sneakers each week. If the number of pairs of sneakers the company sells is increasing at a rate of 25 pairs of sneakers per week, find the rate at which the company's revenue is changing with respect to time when 160 pairs of sneakers are sold each week. In other words, find TS if we know df = 25 pairs of sneakers per week and x = 160 pairs of sneakers. For Exercises 21 - 30, use implicit differentiation to find ay dx 21. x2 + xy3 -3y2 =45 22. - In(y)- xe + 1 = 1 00 23. 3yx-7 + log(y) - 5* Vy = 6In(x) 23 only 1 24. 6 _ 2x 3 + 13 + V7x = 72 25. log, (x) + =4et Vx4x2 26. In(y) -x' -4=2y 27. e2y -5x2 + V12 =-9Vy 28. (7)2 -31) -2(6*)-15y-3 = 105 29. 3x4 - In (32 + 36) = =-In(x) 30. y- 1 10 -2/5 = 2 Vy -83 For Exercises 31 - 39, use implicit differentiation to find dy 31. (35 -y) (0.5x2 -6x) =0 32. (9 Vx+2x) (3)2 + 14y) = 120 33. (4y3 - 242 + y)(15 -3x) =715 29 and 35 -5v4 34. 2x2 - 473 = 30 8.x2 35. 3 Vy -7,0.2 = 6x 2y 36. 10x-1 + x-0.8 = 5x- + 1 37. 412+ 15 = 13 38. (2y3 - x4) = 12x 39. log2 (3x4 - 5y) = -48 For Exercises 40 - 42, find the slope of the line tangent to the graph of the equation at the given point. 40. (x-3x2) (34 -5y) -56 =0 at (-2, 1) 41. 5 23=- 3.x2 21 3" 7y at (1, 1)