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All Textbook Solutions for Calculus and Its Applications (11th Edition)

a. a) Graph the function. b. b) Draw tangent lines to the graph at point whose x-coordinates are 2, 0, and 1. c. c) Find f(x) by determining limx0f(x+h)f(x)h. d. d) Find f(2),f(0,)andf(1). These slopes should match those of the lines you drew in part (b). f(x)=5x22x+7 a. a) Graph the function. b. b) Draw tangent lines to the graph at point whose x-coordinates are 2, 0, and 1. c. c) Find f(x) by determining limx0f(x+h)f(x)h. d. d) Find f(2),f(0,)andf(1). These slopes should match those of the lines you drew in part (b). f(x)=2x2+3x2 a. a) Graph the function. b. b) Draw tangent lines to the graph at point whose x-coordinates are 2, 0, and 1. c. c) Find f(x) by determining limx0f(x+h)f(x)h. d. d) Find f(2),f(0,)andf(1). These slopes should match those of the lines you drew in part (b). f(x)=1x a.Graph the function. b.Draw tangent lines to the graph at point whose x-coordinates are 2, 0, and 1. c.Find f(x) by determining limx0f(x+h)f(x)h. d. d) Find f(2),f(0,)andf(1). These slopes should match those of the lines you drew in part (b). f(x)=2x 17. Find an equation of the tangent line to the graph of at a. (a) ; b. (b) ; c. (c) . See Example 2. 18. Find an equation of the tangent line to the graph of at a. (a) ; b. (b) ; c. (c) . See Example 1. 19. Find an equation of the tangent line to the graph of at a. (a) ; b. (b) ; c. (c) See Example 16. 20. Find an equation of the tangent line to the graph of at a. (a) ; b. (b) ; c. (c) . 21. Find an equation of the tangent line to the graph of at a. (a) ; b. (b) ; c. (c) . 22. Find an equation of the tangent line to the graph of at a. (a) b. (b) c. (c) . Find f(x) for f(x)=mx+b.Find f(x) for f(x)=ax2+bx.For Exercises 25-28, list the graph at which each function is not differentiable.For Exercises 25-28, list the graph at which each function is not differentiable. 26. For Exercises 25-28, list the graph at which each function is not differentiable. 27. For Exercises 25-28, list the graph at which each function is not differentiable. 28. 29. Draw a graph that is continuous, but not differentiable at. Draw a graph that is continuous, with no corners, but not differentiable, at x=1.31. Draw a graph that has a horizontal tangent line at. Draw a graph that is differentiable and has horizontal tangent lines at x=0, x=2 and x=4.Draw a graph that has horizontal tangent lines at x=2 and x=5 and is continuous, but not differentiable, at x=3.Draw a graph that is continuous for all x, with no corners, but not differentiable at x=1 and x=2.35. The postage function. Consider the postage in Exercises 72-76 on p. 105. At what values in the domain is the function not differentiable? 36. The taxicab fare function. Consider the taxicab fare function in Exercises 69-71 on p. 105. At what value is the function not differentiable? The end-of-day values of the Dow Jones Industrial Average for the week of December 9-13, 2013, are graphed below, where x is the day of the month. (Source; Google Finance.) On what did the Dow Jones industrial Average show the greatest rate of crease? On what day did it show the greatest rate of decrease? Give the rates.The end-of-day values of the Dow Jones Industrial Average for the week of December 9-13, 2013, are graphed below, where x is the day of the month. (Source; Google Finance.) Is the function in Exercises 37 differentiable at the given x-values? Why or why not?39. Which of the lines in the following graph appear to be tangent lines? Why or why not? On the following graph, use a colored pencil to draw each secant lines from point P to the point Q. Then use a different colored pencil to draw a tangent line to the curve at p. Describe what happens.For Exercises 41-48, Find for the given function. 41. (See Exercises 49 in Section 1.3.) For Exercises 41-48, Find f(x) for the given function. f(x)=11x (See Exercises 53 in Section 1.3.)For Exercises 41-48, Find f(x) for the given function. f(x)=x5 (See Exercises 50 in Section 1.3.)For Exercises 41-48, Find f(x) for the given function. f(x)=1x2 (See Exercises 52 in Section 1.3.)For Exercises 41-48, Find f(x) for the given function. f(x)=x (See Exercises 8 in Section 1.3.)For Exercises 41-48, Find f(x) for the given function. f(x)=2x+1 (See Exercises 55 in Section 1.3.)For Exercises 41-48, Find for the given function. 47. (See Exercises 56 in Section 1.3.) For Exercises 41-48, Find f(x) for the given function. f(x)=ax2+bx+c (See Exercises 47 in Section 1.3.)49. Consider the function given by . a. a) For what x-value(s) is the function not differentiable? b. b) Find . 50. Consider the function g given by . a. a) For what x-value(s) is this function not differentiable? b. b) What is? Describe the simplest way to determine this. Consider the function k given by k(x)=|x3|+2. a. a) For what x-value(s) is the function not differentiable? b. b) Evaluate k(0),k(1),k(4),andk(10).52. Consider the function k given by . a. For what x-value(s) is this function not differentiable? b. Evaluate Let f(x)=x2+4x+3x+1=(x+1)(x+3)x+1=x+3. A student recognizes that this function can be simplified as y=x+3 Since y=x+3 is a line with slope 1. The student makes the following conclusions; f(2)=1,f(1)=1,f(0)=1,f(1)=1. Where did the student make an error?54. Let. A student graphs this function, and the graph appears to be continuous for all real number x. The student concludes that g is differentiable for all x, which is false. Identify the error, and explain why the conclusion is false. What is the correct conclusion regarding the differentiability of g Let F be a function given by F(x)={x2+1,forx2,2x+1,forx2. a. a) Verify that F is continuous at x=2. b. b) Is F different at x=2? Why or why not?Let G be a function given by G(x)={x3,forx1,3x2,forx1. a. Verify that G is continuous at x=1 b. Is G differentiable at x=1? Why or why not?Let H be a function given by H(x)={2x2+x,forx3,mx+b,forx3. Determine the values of m and b that make H different at x=3.Use a calculator to check your answer to Exercises 17-22. Find an equation of the tangent line to the graph of f(x)=x3 at a. (a) (2,8); b. (b) (0,0); c. (c) (4,64). See Example 2.59E Use a calculator to check your answer to Exercises 17-22. Find an equation of the tangent line to the graph of f(x)=2/x at a. (a) (1,2); b. (b) (1,2); c. (c) (100,0.02). See Example 16.61E Use a calculator to check your answer to Exercises 17-22. Find an equation of the tangent line to the graph of f(x)=x22x at a. (a) (2,8); b. (b) (1,1); c. (c) (4,8).58-63. Use a calculator to check your answer to Exercises 17-22. 63. Find an equation of the tangent line to the graph of at a. (a) b. (b) c. (c) . Business: growth of an investment. A company determines that the value of an investment after t years is V, in millions of dollars, where V is given by V(t)=5t330t2+45t+5t. Note: Calculate often use only the variables y and x, so you may to change the variables. a. a) Graph V over the interval [0,5] b. b) Find the equation of the secant line passing through the point (1,V(1)) and (5,V(5)). Then graph this secant line using the same axes as in part (a). c. c) Find the average rate of change of the investment between year 1 and year 5. d. d) Repeat part (b) and (c) for the following pairs of point; (1,V(1)) and (4,V(4)); (1,V(1)) and (3,V(3)) (1,V(1)) and (1.5,V(1.5)). e. e) What appears to be the slope of the tangent line to the point (1,V(1))? f. Approximate the rate at which the value of the investment is changing at t=1 yr.Use a calculate to determine where f(x), does not exist, if f(x)=x53.Find dydx. y=x8 Find dydx. y=x7 Find. 3. Find. 4. Find. 5. Find. 6. Find. 7. Find. 8. Find. 9. Find dydx. y=x6 Find dydx. y=3x5 Find. 12. Find. 13. Find dydx. y=x3+3x2 Find. 15. Find. 16. Find. 17. Find. 18. Find. 19. Find. 20. Find. 21. Find. 22. Find dydx. y=3x4 y=4x5 Find. 24. Find each derivative. 25. Find each derivative. ddx(x3+4x)Find each derivative. 27. Find each derivative. ddx(x34)Find each derivative. ddx(5x27x+3)Find each derivative. 30. Find 31. Find f(x). f(x)=0.6x1.5 Find 33. Find f(x). f(x)=2x3 Find 35. Find f(x). f(x)=47x3 Find 37. Find f(x). f(x)=5xx2/3 Find f(x). f(x)=7x14 Find 40. Find f(x). f(x)=x3/23 Find 42. Find f(x). f(x)=0.01x2+0.4x+500.02x+0.4 Find f(x). f(x)=0.01x20.5x+700.02x0.5 Find y y=x3/43x2/3+x5/4+2x434x7/42x1/3+54x1/48x5 Find 46. Find y y=x7+7x Find 48. Find y If f(x)=x,findf(4).Find 50. If. Find y If y=x+2x3,finddydx|x=1 Find 52. If Find 53. If Find 54. If Find 55. If Find 56. If 57. Find an equation of the tangent line to the graph of a. at b. at c. at Find an equation (in y=mx+b form) of the tangent line to the graph of f(x)=x32x+1 a. at (2,5) b. at (1,2) c. at (0,1)59. Find an equation of the tangent line to the graph of a. at b. at c. at Find an equation of the tangent line to the graph of f(x)=1x2 a. at (1,1) b. at (3,19) c. at (2,14)For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=x2+4 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=x23 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. 63. For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=x3+1 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. 65. For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=3x25x+4 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=0.01x2+0.4x+50 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=0.01x20.5x+70 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=2x+5 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=2x+4 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. 71. For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. 72. For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. 73. For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=x3+x2+5x1 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=x36x+1 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. y=13x33x+2 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. f(x)=13x33x2+9x9 For each function, find the point on the graph at which the tangent line is horizontal. If none exist, state that fact. 78. For each the function, find the point on the graph at which the tangent line has slope 1. 79. For each the function, find the point on the graph at which the tangent line has slope 1. 80. For each the function, find the point on the graph at which the tangent line has slope 1. y=0.01x2+2x For each the function, find the point on the graph at which the tangent line has slope 1. y=0.025x2+4x For each the function, find the point on the graph at which the tangent line has slope 1. 83. For each the function, find the point on the graph at which the tangent line has slope 1. y=13x3+2x2+2x 85. Heading wound. The circumference C, in centimeters, of a heading wound is approximated by where r is the wound’s radius, in centimeters. a. Find the rate of change of the circumference with respect to the radius. 6.28 cm b. Find. c. Explain the meaning of your answer to part (b) 86. Heading wound. The circular area A, in square centimeters, of a heading wound is approximated by where r is the wound’s radius, in centimeters. a. Find the rate of change of the area with respect to the radius. b. Find. c. Explain the meaning of your answer to part (b). 87. Growth of a baby. The median weight of a boy whose age is between 0 and 36 month is approximated by, where t is in month and w is in pounds. (Source; Centers for Disease Control. Developed by the National Center for Health Statistics in Collaboration with the National Center for Chronic Disease Prevention and Health Promotion, 2000, Rechecked 2014) Use this approximation to find the following; a. The rate of change of weight with respect to time b. The weight of a boy at age 10 month c. The rate of change of a boy’s weight with respect to time at age 10 month 88E 89. Heart rate. The equation can be used to determine the heart rate, R, of a person whose heart pumps 6000 milliliters (mL) of blood per minute and v milliliters of blood per beat. (Source: Mathematics Teacher, Vol. 99, No.4, November 2005.) a. Find the rate of change of heart rate with respect to v, the output per beat. b. Find the heart rate at per beat. c. Find the rate of change at per beat. 90E Population growth rate. In t year, the population of Kingsville grows from 100,000 to a size P given by P(t)=100,000+2000t2. a. Find the growth rate, dP/dt. b. Find the population after 10yr. c. Find the growth rate at t=10. d. Explain the meaning of your answer to part(c).Median age of women at first marriage. The median age of women at first marriage is approximated by A(t)=0.08t+19.7, where A(t) is the median age of women marrying for the first time at t year after 1950. a. Find the rate of change of the median age A with respect to time t. b. Explain the meaning of your answer to part(a).93E Super Bowl ticket prices. The of a ticket to the Super Bowl t years after 1967 can be estimated by p(t)=0.696t213.290t+61.857. (Source; based on data from extrastard.si.com.) a. use the function to predict the price of a Super Bowl ticket in 2014. b. Find the rate of change of the ticket price with respect to the year, dp/dt. c. At what rate were ticket prices changing in 2014?For Exercises 95 and 96, find the interval(s) for which f(x) is positive, f(x)=x24x+1 For Exercises 95 and 96, find the interval(s) for which f(x) is positive, f(x)=13x3x23x+5 Find the points on the graph of y=x443x24 at which the tangent line is horizontal.Find the point on the graph of y=2x6x42 at which the tangent line is horizontal.Use the derivative to help explain why f(x)=x5+x3 increases for all x in (,).100E 101. Use the derivative to help explain why decreases for all x in. Use the derivative to help explain why f(x)=x3+ax increases for all x in (,) when a0 but not when a0.Find Each function can be different using the rules developed in this section, but some algebra may be required beforehand. 103. 104E Find dy/dx Each function can be different using the rules developed in this section, but some algebra may be required beforehand. y=x5x3x2 Find dy/dx Each function can be different using the rules developed in this section, but some algebra may be required beforehand. y=x5xx2 Find Each function can be different using the rules developed in this section, but some algebra may be required beforehand. 107. Find Each function can be different using the rules developed in this section, but some algebra may be required beforehand. 108. Find Each function can be different using the rules developed in this section, but some algebra may be required beforehand. 109. Find dy/dx Each function can be different using the rules developed in this section, but some algebra may be required beforehand. y=(x+1)3 When might Leibniz notation be more convenient than function-notation?112E 113E 114E 115E 116E 117E Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. y=x9x4 Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. y=x5x6 Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. 3. Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. 4. Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. 5. Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. G(x)=4x4(x3+5x)Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. 7. Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. y=(4x+3)x3 Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. f(x)=(2x+5)(3x24x+1)Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. 10. Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. F(t)=(t+2)(3t4t+7)Differentiate two ways; first, by using the Product Rule; then by multiplying the expression before differentiating compare your results as check. Use a graphing calculate to check your results. 12. Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. y=x6x4 Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. 14. Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. 15. Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. f(x)=2x5+x2x Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. G(x)=8x312x1 Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. 18. Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. 19. Differentiate two ways; first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your result as a check. Use a graphing calculator to check your results. y=t225t5 Differentiate each function. g(x)=(5x2+4x3)(2x23x+1)Differentiate each function. 22. Differentiate each function. y=5x212x3+3 Differentiate each function. 24. Differentiate each function. 25. Differentiate each function. G(x)=(8x+x)(5x2+3)Differentiate each function. 27. Differentiate each function. f(t)=t5+2t2t4 Differentiate each function. G(x)=(5x4)2 Differentiate each function. 30. [Hint: ] Differentiate each function. y=(x34x)2 Differentiate each function. y=(3x24x+5)2 Differentiate each function. f(x)=6x4(6x3+10x28x+3)Differentiate each function. 34. Differentiate each function. F(t)=(t+2t)(t23)Differentiate each function. G(x)=(3t5t2)(t5t)Differentiate each function. y=x31x2+1+4x3 Differentiate each function. y=x2+1x315x2 Differentiate each function. 39. Differentiate each function. y=x+4x35 Differentiate each function. f(x)=x1x+x1 Differentiate each function. f(x)=xx1+1 Differentiate each function. F(t)=1t4 Differentiate each function. 44. Differentiate each function. f(x)=3x25xx21 Differentiate each function. 46. Differentiate each function. g(x)=t2+3t+5t2+2t+4 Differentiate each function. 48. 49. Find an equation of the tangent line to the graph of at (a) ; (b) . Find an equation of the tangent line to the graph of y=x/(x+1) at (a) x=1; (b) x=14.51. Find an equation of the tangent line to the graph of at (a) ; (b). Find an equation of the tangent line to the graph of y=4x/(1+x2) at (a) (0,0); (b) (1,2).Average cost. Prestons Leatherworks finds that cost, in dollars, of producing x belts is given by C(x)=750+34x0.068x2. Find the rate at which average cost is changing when 175 belts have been produced.54. Average cost. Tongue-Tied Sauces, Inc, finds that the cost, in dollars, of producing x bottles of barbecue sauce is given by . Find the rate at which average cost is changing when 81 bottles of barbecue sauce have been produced. Average revenue. Prestons Leatherworks find that the revenue, in dollars, from the sale of x belts is given by R(x)=45x9/10. Find the rate at which average revenue is changing when 175 belts have been produced and sold.56. Average revenue. Tongue-Tied Sauces, Inc, finds that the revenue, in dollars, from the sale of x bottles of barbecue sauce is given by. Find the rate at which average is changing when 81 bottles of barbecue sauce have been produced and sold. Average profit. Use the information in Exercises 53 and 55 to determine the rate at which Prestons Leatherworks average profit per belt is changing when 175 belts have been produced and sold.Average profit. Use the information in exercises 54 and 56 to determine the rate at which Tongue-Tied Sauces average profit per bottle of barbecue sauce is changing when 81 bottles have been produced and sold.59. Average profit. Sparkle pottery has determined that the cost, in dollars, of producing x vases is given by . If the revenue from the sale of x vases is given by , find the rate at which average profit per vase is changing when 50 vases have been made and sold. 60. Average profit. Cruzin’ Boards has found that the cost, in dollars of producing x skateboards is given by . If the revenue from the sale of x skateboards is given by , find the rate at which average profit per skateboards is changing when 20 skateboards have been built and sold. Gross domestic produced. The U.S. gross domestic produced (in billions of dollars) can be approximated by P(t)=567+t(36t0.6104). where t is the number of the years since 1960. (Source U.S. Bureau of Economic Analysis.) a. Find P(t). b. Find P(45). c. In words, explain what P(45) represents.Population growth. The population P, in thousands, of the town of Coyote Wells is given by P(t)=500t2t2+9, where t is the time, in years. a. Find the growth rate. b. Find the population after 12 yr. c. Find the growth rate at t=12yr.63E Differentiate each function. 64. (Hint: Simplify before differentiating.) Differentiate each function. 65. Differentiate each function. 66. Differentiate each function. g(x)=(x38)x2+1x21 Differentiate each function. f(t)=(t5+3)t31t3+1 Differentiate each function. f(x)=(x1)(x2+x+1)x43x35 Let f(x)=xx+1 and g(x)=1x+1. a. Compute f(x). b. Compute g(x). c. c) What can you conclude about f and g on the basis of your results from (a) and (b)?71. Let and . a. Compute . b. Compute . c. c) What can you conclude about the graphs of f and g on the basis of your results from part (a) and (b)? Write a rule for finding the derivative of f(x)g(x)h(x). Describe the rule in as few words as possible.Is the derivative of the reciprocal of f(x) the reciprocal of the derivative of f(x)? Why or why not?Sensitivity. The reaction R of the body to a dose Q of medication is often represented by the general function R(Q)=Q2(k2Q3) where k is a constant and R is in millimeters of mercury (mmHg) if the reaction is a change in blood pressure or in degrees Fahrenheit (F) if the reaction is a change in temperature. The rate of change dR/dQ is defined to be the bodys sensitivity to the medication. a. Find a formula for the sensitivity. b. b) Explain the meaning of your answer to part (a).75. A proof of the Product Rule appears below. Provide a justification for each step. a. Definition of derivative b. Adding and subtracting the same quantify is the same as adding 0. c. The limit of a sum is the sum of the limits. d. e. The limit of a product is the product of the limit and . f. Definition of derivative g. Using Leibniz notation 76. Business. Refer to Exercises 54, 56, and 58. At what rate is Tongue-Tied Sauces’ profit changing at the break-even point? At what rate is the average profit per bottle of barbecue sauce changing at that point? 77. Business. Refer to Exercises 53, 55, and 58, At what rate is Preston’s Leatherworks’ profit changing at the breakeven point? At what rate is the average profit per belt changing at that point? For the function in each of Exercises 78-83, graph f and f Then estimate points at which the tangent line to f is horizontal, If no such point exists, state that fact f(x)=x2(x2)(x+2)For the function in each of Exercises 78-83, graph f and Then estimate points at which the tangent line to f is horizontal, If no such point exists, state that fact 79. For the function in each of Exercises 78-83, graph f and f Then estimate points at which the tangent line to f is horizontal, If no such point exists, state that fact f(x)=x31x2+1 For the function in each of Exercises 78-83, graph f and Then estimate points at which the tangent line to f is horizontal, If no such point exists, state that fact 81. For the function in each of Exercises 78-83, graph f and Then estimate points at which the tangent line to f is horizontal, If no such point exists, state that fact 82. For the function in each of Exercises 78-83, graph f and f Then estimate points at which the tangent line to f is horizontal, If no such point exists, state that fact f(x)=4xx2+1 Use a graph to decide which of the following seems to be the correct derivative of the function in Exercises 83. y1=2xy2=44xx2+1y3=44x2(x2+1)2y4=4x24(x2+1)2y3 Differentiate each function. 1. (Check by expanding and then differentiating.) Differentiate each function. y=(2x+1)2 (Check by expanding and then differentiating.)Differentiate each function. y=(7x)55 Differentiate each function. 4. Differentiate each function. 5. Differentiate each function. 6. Differentiate each function. y=3x24 Differentiate each function. 8. Differentiate each function. 9. Differentiate each function. y=(8x26)40 Differentiate each function. 11. Differentiate each function. y=(x+5)7(4x1)10 Differentiate each function. y=1(4x+5)2 Differentiate each function. y=1(3x+8)2 Differentiate each function. y=4x2(7+5x)3 Differentiate each function. y=7x3(49x)5 Differentiate each function. f(x)=(3+x3)5(1+x7)4 Differentiate each function. 18. Differentiate each function. f(x)=x2+(200x)2 Differentiate each function. f(x)=x2+(100x)2 Differentiate each function. G(x)=2x13+(4xx)2 Differentiate each function. 22. Differentiate each function. 23. Differentiate each function. 24. Differentiate each function. 25. Differentiate each function. g(x)=(3x1)7(2x+1)5 Differentiate each function. 27. Differentiate each function. f(x)=x35x+2 Differentiate each function. 29. Differentiate each function. 30. Differentiate each function. 31. Differentiate each function. 32. Differentiate each function. g(x)=3+2x5x Differentiate each function. g(x)=4x3+x Differentiate each function. f(x)=(2x33x2+4x+1)100 Differentiate each function. f(x)=(7x4+6x3x)204 Differentiate each function. 37. Differentiate each function. 38. Differentiate each function. f(x)=x2+xx2x Differentiate each function. 40. Differentiate each function. f(x)=(5x4)7(6x+1)3 Differentiate each function. 42. Differentiate each function. f(x)=12(2x+1)2/3(3x4)5/4 Differentiate each function. y=6x2+x3(x46x)3 Find . 45. Find . 46.

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