MATH 1071Q Quiz: #Wk.7_Section_4.4

2. In xx + 1) 4xx -7 2) 5. 1n In Exercises 7 and 8, find dy/dx implicitly 8. In Exercises 9 and 10, find the second derivative of the funct 10. f 9,f(x) =z?(x + 1)-3x3 Exercises 4.5 See CalcChat.com tor tutor 回饉回Differentiating Logarithmic Functions In Exercises 1-22, find the derivative of the function. See Examples 1, 2, 3, and 4 回 3, y ln(x2 + 3) 7, y = (In x)4 9, f(x)-2x ln x 29. log 31. log 33. loga 6, y = In/1-2x 8, y = (In x2)2 In x 14, y=ln 13, y= In 37. 15. in 18 17

Exercises 2.3 Terms and Concepts 1. What is the name of the rule which states that (r) t)-e- sint-cost where n>0 is an integer? 2. What isInx? 3. Give an example of a function fix) where fx)-fx). 4. Give an example of a function x) where f(x) o. dx derivative rules introduced in this section explain how to compute the derivative of which of the following func- tions? 24.fe) = (1-x)" 25.7(x) = (2-3x), In Exercises 26-31, compute the first four derivatives of the given function & Explain in your own words how to find the third derivative of a function x) 7. Giveanexampleofafunction wherer(x) 0andf"(x)-29, Explain in your own words what the second derivative means 31. fx)-1.100 bn Exercises 32-37, find the equations of the tangent and 0ff(x) describes a position function, then f"(x) describes what kind of function? What kind of function isf"(x)? 9· lines to the graph of the function at the given point. 10. Letx) be a function measured in pounds, where x is mea- sured in feet. What are the units of() Problems in Exercises 11-25,compute the derivative of the given func- Review that 1, approximate the value of e using the tangent ine tofx)-e atx-o 15. fir) e 39. Approximate the value of (3.01) using the tangent line to

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(