EXERCISES 11.1 Find the derivatives of the functions in Problems 1-10 I. f(x) = 4 ln x 3, y=In 8x 23. Find d if y In(Vx1). 24. Finddy ify = In [r(t-x + i)) In Problems 25-38, find y'. 2. y 3 In 4, y = ln 5x 6. f(x) In 8. y=ln (6x + 1) 'In (4x +9) 26, y=x2 ln (2x + 3) 10, y=In (8x3-2x)-2x 11. Find dp/dq ifp=ln (q2+1). 25, y=x-ln x 28,y=l+Inx 30, y ln (3x + 1) 32, y= (in x) 34. y=VIn(3x+1) ds 12. Find ifs In + 1 29, y=ln (x' + 3)? 31, y = (In x)4 In each of Problems 13-18, find the derivative of the function in part (a). Then find the derivative of the func- tion in part (b) or show that the function in part (b) is the same function as that in part (a). 13. (a) y In x In (x 1) 33. y=[In(x' + 3)? 35-y = log, x 37. y 36, y=log,x 38 y = lo& (1-1-r) log (x4-4x3 + 1) In Problems 39-42, find the relative maxima and relative minima, and sketch the graph with a graphing utility to check your results. 39, y=xln x 41. y_x'-81n x (b) y = In 14. (a) y = ln (x-1) + ln (2x + 1) 15. (a) y=11n(x2-1) 16. (a) y-31n (x"-1) 17. (a) y=ln (4x-1)-31nx (b) y= ln [(x-1)(2x + 1)] 40, y=x2 ln x 42, y=ln x-x (b) y In (x"-1)" APPLICATIONS 4x-1 (b) y = In 18. (a) y 3In 43. Marginal cost Suppose that the total cost (in dollas) for a product is given by In (x + 1) C(a) 1500+ 200 In (2x + 1) (b) y= ln ( where x is the number of units produ (a) Find the marginal cost function. (b) Find the marginal cost when 200 units are po duced, and interpret your result ducing more items costs more. What thept (c) Total cost functions always increase D ds dt dy 20. Find ifs = In [r(t2-1)]. of the marginal cost function? Does it this problem? t + 3 21. Find-if)_ In dt 2)/4 44. Investment If money is invested at the the time to increase the investment by a 22. Find a ify=ln(
