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All Textbook Solutions for Calculus: An Applied Approach (MindTap Course List)
Finding the slope of a Graph In Exercises 17-26, use the limit definition to find the slope of the graph of f at the given point. See Examples 3, 4, and 5. f(x)=2x;(4,4)Finding the slope of a Graph In Exercises 17-26, use the limit definition to find the slope of the graph of f at the given point. See Examples 3, 4, and 5. f(x)=x+1;(8,3)Finding a Derivative In Exercises 27-40, use the limit definition to find the derivative to the function. See Examples 6 and 7. f(x)=3Finding a Derivative In Exercises 27-40, use the limit definition to find the derivative to the function. See Examples 6 and 7. f(x)=2Finding a Derivative In Exercises 27-40, use the limit definition to find the derivative to the function. See Examples 6 and 7. f(x)=5xFinding a Derivative In Exercises 27-40, use the limit definition to find the derivative to the function. See Examples 6 and 7. f(x)=4x+1Finding a Derivative In Exercises 27-40, use the limit definition to find the derivative to the function. See Examples 6 and 7. g(s)=13s+232EFinding a Derivative In Exercises 27-40, use the limit definition to find the derivative of the function. See Examples 6 and 7. f(x)=4x25x34EFinding a Derivative In Exercises 27-40, use the limit definition to find the derivative of the function. See Examples 6 and 7. h(t)=t3Finding a Derivative In Exercises 27-40, use the limit definition to find the derivative of the function. See Examples 6 and 7. f(x)=x+237E38E39E40EFinding an Equation of a Tangent Line In Exercises 41-48, find an equation of the tangent line to the graph of f at the given point. Then verify your results by using a graphing utility to graph the function and its tangent line at the point. f(x)=12x2;(2,2)42E43E44E45EFinding an Equation of a Tangent Line In Exercises 41-48, find an equation of the tangent line to the graph of f at the given point. Then verify your results by using a graphing utility to graph the function and its tangent line at the point. f(x)=x+3;(2,1)47E48EFinding an Equation of a Tangent Line In Exercises 49-52, find an equation(s) of the line(s) that is tangent to the graph of f and parallel to the given line. Function Line f(x)=14x2x+y=050E51E52EDetermining Differentiability In Exercises 53-58, describe the x-values at which the function is differentiable. Explain your reasoning. y=| x+3 |54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E71E72E73ECheckpoint 1 Worked-out solution availlable at LarsonAppliedCalculus.com Find the derivative of each function. f(x)=2 y= g(w)=5 s(t)=320.5Checkpoint 2 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of each function. f(x)=x4 b. y=1x3 c. g(w)=w2Checkpoint 3 Worked-out solution available at LarsonAppliedCalculus.com Find the slopes of the graph of f(x)=x3 at x=1, 0, and 1. Find the slopes of the graph of f(x)=x3 at x=1, 0, and 1.Checkpoint 5 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of (a) y=t4 and (b) y=2x5.Checkpoint 6 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of each function. y=94x2 y=9(4x)2Checkpoint 7 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of each function. y=5x y=x4Checkpoint 8 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of each function. f(x)=2x2+5x b. y=x42x c. y=x3+5x1xCheckpoint 9 Worked-out solution available at LarsonAppliedCalculus.com Find the slope of the graph of f(x)=x25x+1 at the point (2,5).Checkpoint 10 Worked-out solution available at LarsonAppliedCalculus.com Find an equation of the tangent line to the graph of f(x)=x2+3x2 at the point (2, 0).Checkpoint 11 Worked-out solution available at LarsonAppliedCalculus.com From 2001 through 2013, the sales per share S (in dollars) for Wal-Mart can be modeled by S=0.1655t2+6.129t+42.04,1t13 Where t represents the year, with t = 1 corresponding to 2001. At what rate was Wal-Marts sales per share changing in 2010? (Source: Wal-Mart Stores, Inc.)In Exercises 1 and 2, evaluate each expression when x = 2. (a) 2x2 (b) (5x)2 (c) 6x-2In Exercises 1 and 2, evaluate each expression when x = 2. (a)1(3x)2(b)14x3(c)(2x)34x2In Exercises 3-6, simplify the expression. 4(3)x3+2(2)xIn Exercises 3-6, simplify the expression. 12(3)x232x1/2In Exercises 3-6, simplify the expression. (14)x3/4In Exercises 3-6, simplify the expression. 13(3)x22(12)x1/2+13x2/3In Exercises 7-10, solve the equation. 3x2+2x=0In Exercises 7-10, Solve the equation. x3x=0In Exercises 7-10, solve the equation. x2+8x20=0In Exercises 7-10, solve the equation. 3x210x+8=0Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y = 3Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. f(x)=8Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y=x5Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. f(x)=1x6Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. h(x)=3x3Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. h(x)=6x5Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y=5x468EFinding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. f(x)=4xFinding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. g(x)=x3Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y=8x312EFinding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. f(x)=4x23x14EFinding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. f(t)=3t2+2t416EFinding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. s(t)=4t42t2+t+3Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y=2x3x2+3x1Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. g(x)=x2/3Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. h(x)=x5/2Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y=4t4/322EFinding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. y=4x2+2x224EUsing Parentheses when Differentiating In Exercises 25-30, find the derivative of the function. See Example 6. Function Rewrite Differentiate Simplify y=27x426EUsing Parentheses when Differentiating In Exercises 25-30, find the derivative of the function. See Example 6. Function Rewrite Differentiate Simplify y=1(4x)328EUsing Parentheses when Differentiating In Exercises 25-30, find the derivative of the function. See Example 6. Function Rewrite Differentiate Simplify y=4(2x)530EDifferentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Function Rewrite Differentiate Simplify y=6xDifferentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Function Rewrite Differentiate Simplify y=3x4Differentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Function Rewrite Differentiate Simplify y=176xDifferentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Function Rewrite Differentiate Simplify y=324x3Differentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Function Rewrite Differentiate Simplify y=8x5Differentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Function Rewrite Differentiate Simplify y=6x23Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. y=x3/2Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. y=x1Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. f(t)=t4;(12,16)Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. f(x)=x1/3;(8,12)Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. f(x)=2x3+8x2x4;(1,3)Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. f(x)=x42x3+5x27x;(1,15)Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. f(x)=12x(1+x2);(1,1)Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. See Examples 3 and 9. f(x)=3(5x)2;(5,0)Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. See Example 10. y=2x4+5x23;(1,0)Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. See Example 10. y=x3+x+4;(2,6)Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. See Example 10. f(x)=x3+x5;(1,2)Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. See Example 10. f(x)=1x23x;(1,2)Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. See Example 10. y=3x(x22x);(2,18)Finding an Equation of a Tangent Line In Exercises 45-50, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. See Example 10. y=(2x+1)2;(0,1)Finding Derivatives In Exercises 51-62, find f(x). f(x)=x24x3x2Finding Derivatives In Exercises 51-62, find f(x). f(x)=6x25x2+7x3Finding Derivatives In Exercises 51-62, find f(x). f(x)=x22x2x4Finding Derivatives In Exercises 51-62, find f(x). f(x)=x2+4x1xFinding Derivatives In Exercises 51-62, find f(x). f(x)=x4/5+xFinding Derivatives In Exercises 51-62, find f(x). f(x)=x1/31Finding Derivatives In Exercises 51-62, find f(x). f(x)=x(x2+1)Finding Derivatives In Exercises 51-62, find f(x). f(x)=(x2+2x)(x+1)Finding Derivatives In Exercises 51-62, find f(x). f(x)=2x34x2+3x2Finding Derivatives In Exercises 51-62, find f(x). f(x)=2x23x+1xFinding Derivatives In Exercises 51-62, find f(x). f(x)=4x33x2+2x+5x2Finding Derivatives In Exercises 51-62, find f(x). f(x)=6x3+3x22x+1xFinding Horizontal Tangent Lines In Exercises 63-66, determine the point(s), if any, at which the graph of the function has a horizontal tangent line. y=x42x2+364EFinding Horizontal Tangent Lines In Exercises 63-66, determine the point(s), if any, at which the graph of the function has a horizontal tangent line. y=12x2+5x66EUsing the Derivative In Exercises 67 and 68, determine the point(s), if any, at which the graph of the function has a tangent line with the given slope. FunctionSlopey=x2+3m=468E69E70E71E72EExploring Relationships In Exercises 71-74, the relationship between f and g is given. Explain the relationship between f and g. g(x)=5f(x)Exploring Relationships In Exercises 71-74, the relationship between f and g is given. Explain the relationship between f and g. g(x)=3f(x)1Revenue The revenue R (in millions of dollars) for Under Armour from 2008 through 2013 can be modeled by R=4.1685t3+175.037t21950.88t+7265.3 where t is the year, with t=8 corresponding to 2008. (Source: Under Armour, Inc.) (a) Find the slopes of the graph for the years 2009 and 2011. (b) Compare your results with those obtained in Exercise 13 in Section 2.1. (c) Interpret the slope of the graph in the context of the problem.Sales The sales S (in millions of dollars) for Fossil from 2007 through 2013 can be modeled by S=2.67538t4+94.0568t31155.203t2+6002.42t97942. where t is the year, with t=7 corresponding to 2007. (Source: Fossil, Group) (a) Find the slopes of the graph for the years 2010 and 2012. (b) Compare your results with those obtained in Exercise 14 in Section 2.1. (c) Interpret the slope of the graph in the context of the problem.77EHOW DO YOU SEE IT? The attendance for four high school basketball games is given by s=f(t), and the attendance for four high school football games is given by s=f(t), where t=1 corresponds to the first game. (a) Which attendance rate, f' or g', is greater at game 1? (b) What conclusion can you make regarding the attendance rates, f' and g', at game 3? (c) What conclusion can you make regarding the attendance rates, f' and g', at game 4? (d) Which sport do you think would have a greater attendance for game 5? Explain your reasoning.79EPolitical Fundraiser A politician raises funds by selling tickets to a dinner for $500. The politician pays $150 for each dinner and has fixed costs of $7000 to rent a dining hall and wait staff. Write the profit P as a function of x, the number of dinners sold. Show that the derivative of the profit function is a constant and is equal to the increase in profit from each dinner sold.81E82E83E84ECheckpoint 1 Worked-out solution available at LarsonAppliedCalculus.com Use the table in Example 1 to find the average rate of change of C over each interval. a. [0, 120] b. [90, 100] c. [90, 120]2CP3CPCheckpoint 4 Worked-out solution available at LarsonAppliedCalculus.com At time t = 0, a diver jumps from a diving board that is 12 feet high with an initial velocity of 16 feet per second. The divers position function is s = 16t2 + 16t + 12. a. When does the diver hit the water? b. What is the divers velocity at impact?5CP6CP7CP8CP1SWU2SWU3SWU4SWU5SWU6SWU7SWU8SWU9SWU10SWU11SWU12SWU1ETrade Deficit The graph shows the values I (in billions of dollars) of goods imported to the United States and the values E (in billions of dollars) of goods exported from the United States from 1980 through 2013. Approximate the average rates of change of I and E during each period. (Source: U.S. Census Bureau) (a) Imports: 1980-1990 (b) Exports: 1980-1990 (c) Imports: 1990-2000 (d) Exports: 1990-2000 (e) Imports: 2000-2010 (f) Exports: 2000-2010 (g) Imports: 1980-2013 (h) Exports: 1980-20133E4E5E6EFinding Rates of Change In Exercises 312, find the average rate of change of the function over the given interval. Compare this rate with the instantaneous rates of change at the endpoints of the interval. f(x)=3x4/3;[ 1,8 ]8E9E10E11E12EConsumer Trends The graph shows the number of visitors V (in thousands) to a national park during a one-year period, where t=1 represents January. (a) Estimate the average rate of change of V over the interval [ 9,12 ] and explain your results. (b) Over what interval is the average rate of change approximately equal to the rate of change at t=8 ? Explain your reasoning.Medicine The graph shows the estimated number of milligrams of a pain medication M in the bloodstream t hours after a 1000-milligram dose of the drug has been given. (a) Estimate the average rate of change of M over the interval [ 1,3 ] and explain your results. (b) Over what interval is the average rate of change approximately equal to the rate of change at t=4 ? Explain your reasoning.Velocity The height s (in feet) at time t (in seconds) of a ball thrown upward from the top of a building is given by s=16t2+30t+250. Find the average velocity over each indicated interval and compare this velocity with the instantaneous velocities at the endpoints of the interval. (a) [0, 1] (b) [1, 2] (c) [2, 3] (d) [3, 4]16EVelocity The height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of a building is given by s = 16t2 + 555. (a) Find the average velocity over the interval [2, 3]. (b) Find the instantaneous velocities when t = 2 and t = 3. (c) How long will it take the coin to hit the ground? (d) Find the velocity of the coin when it hits the ground.Velocity A ball is thrown straight down from the top of a 210-foot building with an initial velocity of - 18 feet per second. (a) Find the position and velocity functions for the ball. (b) Find the average velocity over the interval [ 1,2 ]. (c) Find the instantaneous velocities when t=1 and t=2. (d) How long will it take the ball to hit the ground? (e) Find the velocity of the ball when it hits the ground.19E20E21E22E23E24E25E26E27E28E29E30E31EMarginal revenue The revenue R (in dollars) from renting x apartments can be modeled by R=2x(900+32xx2) (a) Find the marginal revenue when x = 14. (b) Find the additional revenue when the number of rentals is increased from 14 to 15. (c) Compare the results of parts (a) and (b).Marginal Profit The profit P (in dollars) from selling x tablet computers is given by P=0.04x2+25x1500. (a) Find the marginal profit when x = 150. (b) Find the additional profit when the sales increase from 150 to 151 units. (c) Compare the results of parts (a) and (b).Marginal Profit The profit P (in dollars) from selling x units of a product is given by P=36,000+2048x18x2,150x275. Find the marginal profit for each of the following sales. (a) x = 150 (b) x = 175 (c) x = 200 (d) x = 225 (e) x = 250 (f) x = 27535EHealth The temperature T (in degrees Fahrenheit) of a person during an illness can be modeled by the equation T=0.0375t2+0.3t+100.4 where t is time in hours since the person started to show signs of a fever. (a) Use a graphing utility to graph the function. Be sure to choose an appropriate window. (b) Do the slopes of the tangent lines appear to be positive or negative? What does this tell you? (c) Evaluate the function for t=0,4,8,and12. (d) Find dT/dt and explain its meaning in this situation. (e) Evaluate dT/dt for t=0,4,8, and 12. Explain your results.37EProfit The monthly demand function p and cost function C for x magazines downloaded from a digital store are p=50.001xandC=35+1.5x. (a) Find the monthly revenue R as a function of x. (b) Find the monthly profit P as a function of x. (c) Complete the table. x 600 1200 1800 2400 3000 dR/dx dP/dx P39EMarginal Profit When the admission price for a baseball game was $30 per ticket, 36,000 tickets were sold. When the price was raised to $35, only 32,000 tickets were sold. Assume that the demand function is linear and that the marginal and fixed costs for the ballpark owners are $5 and $700,000, respectively. (a) Find the profit P as a function of x, the number of tickets sold. (b) Use a graphing utility to graph P, and comment about the slopes of P when x=18,000,x=28,000,andx=36,000. (c) Find the marginal profits when 18,000 tickets are sold, when 28,000 tickets are sold, and when 36,000 tickets are sold.41EGasoline Sales The number N of gallons of regular unleaded gasoline sold by a gasoline station at a price of p dollars per gallon is given by N=f(p). (a) Describe the meaning of f(2.959). (b) Is f(2.959) usually positive or negative? Explain.Dow Jones Industrial Average The table shows the year-end closing prices p of the Dow Jones Industrial Average (DJIA) from 2000 through 2013, where t is the year, with t=0 corresponding to 2000. (Source: Dow Jones Industrial Average) 0 1 2 3 10,786.85 10,021.50 8341.63 10,453.92 t 4 5 6 7 P 10,783.01 10,717.50 12,463.15 13,264.82 t 8 9 10 11 p 8776.39 10,428.05 11,577.51 12,217.56 t 12 13 P 13,104.14 16,576.66 Spreadsheet at LarsonAppliedCaIculus.com (a) Determine the average rate of change in the value of the DJIA from 2000 through 2013. (b) Estimate the instantaneous rate of change in 2005 by finding the average rate of change from 2003 to 2007. (c) Estimate the instantaneous rate of change in 2005 by finding the average rate of change from 2004 to 2006. (d) Compare your answers for parts (b) and (c). Which interval do you think produced the best estimate for the instantaneous rate of change in 2005?HOW DO YOU SEE IT? Many populations in nature exhibit logistic growth, which consists of four phases, as shown in the figure. Describe the rate of growth of the population in each phase, and give possible reasons as to why the rates might be changing from phase to phase. (Source: Adapted from Levine/Miller, Biology: Discovering Life, Second Edition)Checkpoint 1 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of y=(4x+3x2)(63x).Checkpoint 2 Worked-out solution available at LarsonAppliedCalculus.com Find the derivative of f(x)=(1x+1)(2x+1).3CP4CP5CP6CP7CP8CPIn Exercises 1-10, simplify the expression. 1.(x2+1)(2)+(2x+7)(2x)2SWU3SWU4SWU5SWU6SWU7SWU8SWU9SWU10SWU11SWU12SWU13SWU14SWUUsing the Product Rule In Exercises 1-10, use the Product Rule to find the derivative of the function. See Examples 1, 2, and 3. 1.f(x)=(2x3)(15x)Using the Product Rule In Exercises 1-10, use the Product Rule to find the derivative of the function. See Examples 1, 2, and 3. 2.g(x)=(4x7)(3x+1)Using the Product Rule In Exercises 1-10, use the Product Rule to find the derivative of the function. See Examples 1, 2, and 3. 3.f(x)=(6xx2)(4+3x)4EUsing the Product Rule In Exercises 1-10, use the Product Rule to find the derivative of the function. See Examples 1, 2, and 3. 7.f(x)=x(x2+3)6EUsing the Product Rule In Exercises 1-10, use the Product Rule to find the derivative of the function. See Examples 1, 2, and 3. 7.h(x)=(2x3)(x2+7)8EUsing the Product Rule In Exercises 1-10, use the Product Rule to find the derivative of the function. See Examples 1, 2, and 3. 9.g(x)=(x24x+3)(x2)10EUsing the Quotient Rule In Exercises 11-20, use the Quotient Rule to find the derivative of the function. See Examples 4 and 6. 11.h(x)=xx512E13E14EUsing the Quotient Rule In Exercises 11-20, use the Quotient Rule to find the derivative of the function. See Examples 4 and 6. 15.f(t)=t+6t2816EUsing the Quotient Rule In Exercises 11-20, use the Quotient Rule to find the derivative of the function. See Examples 4 and 6. 17.f(x)=x2+6x+52x118E19E20EUsing the Constant Multiple Rule In Exercises 21-30, find the derivative of the function. See Example 7. Original Function Rewrite Differentiate Simplify 21.f(x)=x3+6x322E23E24EUsing the Constant Multiple Rule In Exercises 21-30, find the derivative of the function. See Example 7. Original Function Rewrite Differentiate Simplify 25.y=73x326EUsing the Constant Multiple Rule In Exercises 21-30, find the derivative of the function. See Example 7. Original Function Rewrite Differentiate Simplify 27.y=4x23x8xUsing the Constant Multiple Rule In Exercises 21-30, find the derivative of the function. See Example 7. Original Function Rewrite Differentiate Simplify 28.y=(3x2+2x)6x3Using the Constant Multiple Rule In Exercises 21-30, find the derivative of the function. See Example 7. Original Function Rewrite Differentiate Simplify 29.y=x34x+32(x1)Using the Constant Multiple Rule In Exercises 21-30, find the derivative of the function. See Example 7. Original Function Rewrite Differentiate Simplify 30.y=x24x+2Finding Derivatives In Exercises 31-46, find the derivative of the function. State which differentiation rule(s) you used to find the derivative. 31.f(x)=(x33x)(2x2+3x+5)32E33E34EFinding Derivatives In Exercises 31-46, find the derivative of the function. State which differentiation rule(s) you used to find the derivative. 35.f(x)=x3+3x+2x2136E37E38EFinding Derivatives In Exercises 31-46, find the derivative of the function. State which differentiation rule(s) you used to find the derivative. 39.g(t)=(2t31)240EFinding Derivatives In Exercises 31-46, find the derivative of the function. State which differentiation rule(s) you used to find the derivative. 41.g(s)=s22s+5sFinding Derivatives In Exercises 31-46, find the derivative of the function. State which differentiation rule(s) you used to find the derivative. 42.f(x)=x35x26xxFinding Derivatives In Exercises 31-46, find the derivative of the function. State which differentiation rule(s) you used to find the derivative. 43.f(x)=(x2)(3x+1)4x+244E45E46EFinding an Equation of a Tangent Line In Exercises 47-54, find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 5. FunctionPointf(x)=(5x+2)(x2+x)(1,0)48E49E50EFinding an Equation of a Tangent Line In Exercises 47-54, find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 5. FunctionPointf(x)=3x2x+1(4,2)Finding an Equation of a Tangent Line In Exercises 47-54, find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 5. FunctionPointf(x)=2x+1x1(2,5)53E54E55E56E57E58E59E60E61E