41 (m2 + 19)/2 – + 19)'/21Now we to the we have(m2 + – + 19)-1/2(2m)](81 + - 9) – (10 · 19)-1/2(2.9)]|10m2PChapter 11 Differentiationbp%3D532upup[(m² + 19)/2?up-m2 + 19||bpupTherefore, from the chain rule,dm m=9= (1)(10.71) = 10.71A direct formula for the marginal-revenueproduct isbpupbp$10.71 per day. Toolaho lo idaunup32. y = 2x+In Problems 1-8, use the chain rule. gunave-isnigh31. y = ▼7x + vA1. If y = u? - 2u and u = x² – x, find dy/dx.PROBLEMS 11.534. y = x(x + 4)4%3D2. If y = 2u³ – 8u and u = 7x – x³ find dylddro rit 2ami 33. y = x° (2x + 3).Solutiom Siatez%3D35. y = 4x²/5x + 137. y = (x² + 2x – 1)°(5x)38. y = x*(x* – 1)540. y = (3x + 2) (4x – 5)2|-39. y = (8x – 1)°(2x + 1)4x - 3|43. If y =and w = 3x – 5, find dy/dxr.1242. y =4. If y = z and z = x – x* + 3, find dy/dx.I- 1-, find dw/dt when t = 1.41. y=8x2 - 36. If z = u² + Vũ +9 and u = 2s² – 1, find dz/ds when s =-1.gedw p7. If y = 3w² – 8w +4 and w = 2x² + 1, find dy/dx when x =5. If w = u and u =1GAGU%3D44. y=3/I + xx2 + 2= 0.43. y=(4x – 2)4|2x - 546. y =45. y =(x² + 4)³(8x – 1)5(3x – 1)³8. If y = 2u + 3u? + 5u – 1 and u = 3x + 1, find dy/dx when-48. y = (x – 3)³ (x + 5)--%3DIn Problems 9-52, find y'.47. y=obh do nav 49. y = 6(5x² + 2)/xª + 5-10. y= (x² – 4)*s bas50. y= 6+3x - 4x(7x + 1)|9. y= (3x+ 2)6ngod o12. y = (x2 + xr)(2x2 + 1)4%3D11. y= (3+2x³)58t-7\213. y = 5(r³ – 3r² +2x)!000114. y=51. y = 8t +%3D24.%3D(2x + 6)(7x – 5)15. y= (x² – 2)-317. y= 2(x² + 5x – 2)-5/716. y= (2x³ – 8x)-12|52. y =18. y = 3(5x – 2x³)-S/3(2x + 4)2810022. y= V&r2 ー119. y = 5x2 –x0018 20y = v3x² – 7In Problems 53 and 54, use the quotient rule and power rule tofind y'. Do not simplify your answer.%3D21. y = 2x – 13-%3DVx+2(4x²- 1)9x- 323. y = 4/(x? +1) l 24. y =7/(r5 - 3)5e(3x + 2)°(x + 1)ª(x² – 7)3%3DSTO Si brn o 53. y =54. y =9.2r2 – x + 13.26. y =25. y =%3Dx4 +21%3D1.(x² – 3x)²55. If y = (5u + 6)³ and u = (x² + 1), find dy/dx when x 056. If z = 2y² – 4y + 5, y = 6x – 5, and x = 21, find dz/dt wht = 1.%3D27. y=28. y =%3D%3D3.(3x² – x)2/329. y =4.57. Find the slope of the curve y = (x² - 7x-8) at the point(8, 0).30. y =9x² + 1%3D

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37. y= (x² + 2x – 1)³(5x) | || 39. y = (8x – 1)°(2x + 1)4 || 12 x - 3 Th 41. y = n gedw X +2 r+ 1