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All Textbook Solutions for Finite Mathematics and Applied Calculus (MindTap Course List)

Marginal Profit Your monthly profit (in dollars) from selling magazines is given by P=5x+x where x is the number of magazines you sell in a month. If you are currently selling 50 magazines per month, find your profit and your marginal profit. Interpret your answers.Marginal Profit Your monthly profit (in dollars) from your newspaper route is given by P=2nn where n is the number of subscribers on your route. If you currently have 100 subscribers, find your profit and your marginal profit. Interpret your answers.Marginal Revenue: Pricing Tuna Assume that the demand equation for tuna in a small coastal town is given by p=20,000q1.5(200q800), where p is the price (in dollars) per pound of tuna and q is the number of pounds of tuna that can be sold at the price p in one month. a. Calculate the price that the towns fishery should charge for tuna to produce a demand of 400 pounds of tuna per month. b. Calculate the monthly revenue R as a function of the number of pounds of tuna q. c. Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds per month, and interpret the results. d. If the town fisherys monthly tuna catch amounted to 400 pounds of tuna and the price is at the level in part (a), would you recommend that the fishery raise or lower the price of tuna to increase its revenue?20E 21E 22E 23E 24E Advertising Cost Your company is planning to air a number of television commercials during the ABC Television Networks presentation of the Academy Awards. ABC is charging your company $1.9 million per 30-second spot. Additional fixed costs (development and personnel costs) amount to $500,000, and the network has agreed to provide a discount of 100,000x for x television spots. a. Write down the cost function C, marginal cost function C, and average cost function C. b. Compute C(3) and C(3). (Round all answers to three significant digits.) Use these two answers to say whether the average cost is increasing or decreasing as x increases.26E 27E Taxation Schemes To raise revenues during the recent recession, the governor of your state proposed the following taxation formula: T(i)=0.001i0.5, where i representstotal annual income earned by an individual in dollars and T(i) is the income tax rate as a percentage of total annual income. (Thus, for example, an income of $50,000 per year would be taxed at about 22%, while an income of double that amount would be taxed at about 32%.)19 a. Calculate the after-tax (net) income N(i) anindividual can expect to earn as a function of income i. b. Calculate an individuals marginal after-tax income at income levels of $100,000 and $500,000. c. At what income does an individuals marginal after-tax income become negative? What is the after-tax income at that level, and what happens at higher income levels? d. What do you suspect is the most anyone can earn after taxes? (See the footnote.)29E 30E 31E 32E 33E 34E 35E For the cost function C(x)=mx+b themarginal cost of producing the 1,001st item is (A) equal to (B) approximately equal to (C) always slightly greater than (D) always slightly less than the actual cost of producing the 1,001st item.37E 38E 39E 40E 41E 42E 43E 44E 45E 46E In Exercises 112 (a) Calculate the derivative of the given function without using either the product rule or the quotient rule. (b) Use the product rule or the quotient rule to find the derivative. Check that you obtain the same answer. [HINT: See Quick Examples 1 and 2.] f(x)=3x 2E In Exercises 112 (a) Calculate the derivative of the given function without using either the product rule or the quotient rule. (b) Use the product rule or the quotient rule to find the derivative. Check that you obtain the same answer. [HINT: See Quick Examples 1 and 2.] g(x)=xx2 In Exercises 112 (a) Calculate the derivative of the given function without using either the product rule or the quotient rule. (b) Use the product rule or the quotient rule to find the derivative. Check that you obtain the same answer. [HINT: See Quick Examples 1 and 2.] g(x)=xx In Exercises 112 (a) Calculate the derivative of the given function without using either the product rule or the quotient rule. (b) Use the product rule or the quotient rule to find the derivative. Check that you obtain the same answer. [HINT: See Quick Examples 1 and 2.] h(x)=x(x+3)In Exercises 112 (a) Calculate the derivative of the given function without using either the product rule or the quotient rule. (b) Use the product rule or the quotient rule to find the derivative. Check that you obtain the same answer. [HINT: See Quick Examples 1 and 2.] h(x)=x(1+2x)In Exercises 112 (a) Calculate the derivative of the given function without using either the product rule or the quotient rule. (b) Use the product rule or the quotient rule to find the derivative. Check that you obtain the same answer. [HINT: See Quick Examples 1 and 2.] r(x)=100x2.1 8E 9E 10E 11E 12E 13E 14E In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=x3(1x2)In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=x5(1x)17E In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=(4x1)2 In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=4x5x2 In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=3x3x+2 21E In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=3x92x+4 23E 24E 25E 26E In Exercises 13-28, calculate dydx. Simplify your answer. [HINT: See Example 1 and 2.] y=xx 28E 29E 30E In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(2x0.5+4x5)(xx1)32E 33E 34E In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(x3.2+3.2x)(x2+1)In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(x2.17+2x2.1)(7x1)In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=x2(2x+3)(7x+2) [HINT: See Example 1 (b).]In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=x(x23)(2x2+1) [HINT: See Example 1 (b).]In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(5.3x1)(1x2.1)(x2.33.4)In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(1.1x+4)(x2.1x)(3.4x2.1)In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(x+1)(x+1x2)In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(4x2x)(x2x2)43E In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=3x29x+112x+4 45E 46E 47E 48E In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=x+1x1 50E In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(1x+1x2)x+x2 52E In Exercises 29-56, calculate dydx. You need not expand your answers. [HINT: See Example 1 and 2.] y=(x+3)(x+1)3x1 [HINT: See Example 2(b).]54E 55E 56E 57E In Exercises 57-62, compute the indicated derivatives. ddx[(x2+x3)(x+1)]In Exercises 57-62, compute the indicated derivatives. ddx[(x3+2x)(x2x)]|x=2 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E 70E 71E In Exercises 71-76, find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate. f(x)=(x0.5+1)(x2+x);x=1 73E 74E 75E 76E Revenue The monthly sales of Sunny Electronics new sound system are given by q(t)=2,000t100t2 units per month, t months after its introduction. The price Sunny charges is p(t)=1,000t2 dollars per sound system, t months after introduction. Find the rate of change of monthly sales, the rate of change of the price, and the rate of change of monthly revenue 5 months after the introduction of the sound system. Interpret your answer. [HINT: See Example 4(a).]Revenue The monthly sales of Sunny Electronics new iSun media player is given by q(t)=2,000t100t2 units per month, t months after its introduction. The price Sunny charges is p(t)=100t2 dollars per iSun, t months after introduction. Find the rate of change of monthly sales, the rate of change of the price, and the rate of change of monthly revenue 6 months after the introduction of the iSun. Interpret your answer. [HINT: See Example 4(a).]Saudi Oil Revenues The price of crude oil during the period 2000-2010 can be approximated by P(t)=6t+18dolloarsperbarrel(0t10) In year t, where t=0 represents 2000. Saudi Arabias crude oil production over the same period can be approximated by P(t)=0.036t2+0.62+8millionbarrelsperday(0t10). Use these models to estimate Saudi Arabias daily oil revenue and also its rate of change in 2008. (Round your answer to the nearest $1 million.)Russian Oil Revenues The price of crude oil during the period 20002010 can be approximated by P(t)=6t+18dolloarsperbarrel(0t10) In year t, where t=0 represents2000.Russias crude oil production over the same period can be approximated by P(t)=0.086t2+1.2t+5.5millionbarrelsperday(0t10) Use these models to estimate Russias daily oil revenue and also its rate of change in 2005. (Round your answers to the nearest $1 million.)Revenue Dorothy Wagner is currently selling 20 I Calculus T-shirts per day, but sales are dropping at a rate of 3 per day. She is currently charging $7 per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by $1 per day. How fast, and in what direction, is her daily revenue currently changing?82E 83E 84E Fuel Economy Your muscle cars gas mileage (in miles per gallon) is given as a function M(x) ofspeed x in miles per hour, where M(x)=3,000x+3,600x1. Calculate M(x) andthen M(10),M(60),andM(70). What do the answers tell you about your car?86E 87E Oil Imports from Mexico Daily oil production in Mexico and daily U.S. oil imports from Mexico during 2000 2004 could be approximated by P(t)=3.0+0.13tmillionbarrels(0t4)I(t)=1.4+0.06tmillionbarrels(0t4), where t is time in years since the start of 2000. a. What are represented by the function P(t)I(t) and I(t)/P(t)? b. Compute ddt[I(t)P(t)]|t=3 totwo significant digits. What does the answer tell you about oil imports from Mexico?89E 90E 91E Biology-Reproduction Another model, the predator satiation model for population growth, specifies that the reproductive rate of an organism as a function of the total population varies according to the following formula: R(p)=rp1+kp, where p is the total population in thousands of organisms, r and k are constants that depend on the particular circumstances and the organism being studied, and R(p) is the reproduction rate in thousands of organisms per hour. k=0.2andr=0.08,, find R(p) and R(2). Interpret the result.Embryo Development Bird embryos consume oxygen from the time the egg is laid through the time the chick hatches. For a typical galliform bird egg, the oxygen consumption (in milliliters) t days after the egg was laid can be approximated by C(t)=0.016t4+1.1t311t3+3.6t(15t30) (An egg will usually hatch at around t=28.) Suppose that at time t=0 youhave a collection of 30 newly laid eggs and that the number of eggs decreases linearly to zero at time t=30 days. How fast is the total oxygen consumption of your collection of embryos changing after 25 days? (Round your answers to two significant digits.) Comment on the result. [HINT: Total oxygen consumption=Oxygen consumptionper eggNumber ofeggs.]Embryo Developmen Turkey embryos consume oxy- gen from the time the egg is laid through the time the chick hatches. For a brush turkey the oxygen consumption (in milliliters) t days after the egg was laid can be approximated by C(t)=0.0071t4+0.95t322t3+95t(25t50) (An egg will typically hatch at around t=50.) Suppose that at time t=0 youhave a collection of 100 newly laid eggs and that the number of eggs decreases linearly to zero at time t=50 days. How fast is the total oxygen consumption of your collection of embryos changing after 40 days? (Round your answer to two significant digits.) Interpret the result. [HINT: Total oxygen consumption=Oxygen consumptionper eggNumber ofeggs.]95E 96E 97E 98E 99E 100E 101E 102E 103E 104E 105E 106E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(2x+1)2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(3x1)2 3E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(2x1)2 5E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(1x)1 7E 8E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=13x1 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=1(x+1)2 11E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(x3x)3 13E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(2x3+x)2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] g(x)=(x23x1)5 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] g(x)=(2x2+x+1)3 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] h(x)=1(x2+1)3 [HINT: See Example 2.]In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] h(x)=1(x2+x+1)2 [HINT: See Example 2.]In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] r(x)=(0.1x24.2x+9.5)1.5 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] r(x)=(0.1x4.2x1)0.5 21E 22E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=1x2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=x+x2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=3x6 [HINT: See Example 1 (d).]In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=5x+1 [HINT: See Example 1 (d).]In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=x3+5x In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=xx4 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] h(x)=2[(x+1)(x21)]1/2 [HINT: See Example 3.]In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] h(x)=3[(2x1)(x1)]1/3 [HINT: See Example 3.]In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] h(x)=(3.1x2)21(3.1x2)2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] h(x)=(3.1x2213.1x2)2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=[(6.4x1)2+(5.4x2)3]2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=[(6.4x3)2+(4.3x1)]2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(x23x)2(1x2)0.5 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(3x2x)(1x2)0.5 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] s(x)=(2x+43x1)2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] s(x)=(3x92x+4)3 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] g(z)=(z1+z2)3 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] g(z)=(z21+z)2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=[(1+2x)4(1x)2]3 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=[(3x1)2+(1x)5]2 In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(3x1)3x1 44E 45E 46E 47E 48E In Exercises 1-50, calculate the derivate of the function. [HINT: See Example 1.] f(x)=(1+(1+(1+2x)3)3)3 50E In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] y=u2,u=x+2;dydx In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] y=u3,u=x1;dydx In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] y=x2+x,x=2t1;dydt 54E In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] y=3x2;dxdy 56E 57E In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] y=x3;dxdy 59E 60E In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] x=t2,y=6t+1,t0;dydx 62E In Exercises 51-66, compute the indicated derivative using the chain rule. [HINT: See Quick Example 3, 6, and 7.] y=3x22x;dxdy|x=1 64E 65E 66E In Exercises 67-74, find the indicated derivative. In each case the independent variable is a (unspecified) differentiable function of t. [HINT: See Quick Example 4.] y=x100+99x1.Finddydt.In Exercises 67-74, find the indicated derivative. In each case the independent variable is a (unspecified) differentiable function of t. [HINT: See Quick Example 4.] y=x0.5(1+x).Finddydt.In Exercises 67-74, find the indicated derivative. In each case the independent variable is a (unspecified) differentiable function of t. [HINT: See Quick Example 4.] s=1r3+r0.5.Finddsdt.70E In Exercises 67-74, find the indicated derivative. In each case the independent variable is a (unspecified) differentiable function of t. [HINT: See Quick Example 4.] V=43r3.FinddVdt.72E In Exercises 67-74, find the indicated derivative. In each case the independent variable is a (unspecified) differentiable function of t. [HINT: See Quick Example 4.] y=x3+1x,x=2whent=1,dxdt|t=1=1Finddydt|t=1 74E Crude Oil Prices The price per barrel of crude oil in the period 19802013, in constant 2014 dollars, can be approximated by P(t)=0.27(t1980)28.6(t1980)+93dollars(1980t2013), where t is the year.30 Find P(t)andP(2010). What does the second answer tell you about the price of crude oil?Median Home Prices The median home price in the United States over the period January 2010January 2015 can be approximated by P(t)=4.5(t2010)215(t2010)+180thousanddollars(2010t2015), where t is the year. Find P(t)andP(2011). What does the second answer tell you about home prices?Marginal Profit Your monthly profit (in dollars) from selling magazines is given by P=5x+2x+10, where x is the number of magazines you sell in a month. If you are currently selling 50 magazines per month, find your profit and your marginal profit. Interpret your answers.78E 79E 80E Marginal Profit Paramount Electronics has an annual profit given by P=100,000+5,000q0.25q2dollers, where q is the number of laptop computers it sells each year. The number of laptop computers it can make and sell each year depends on the number n of electrical engineers Paramount employs, according to the equation q=30n+0.01n2. Use the chain rule to find dPdn|n=10 andinterpret the result. [HINT: See Example 4.]Marginal Profit Refer back to Exercise 81. The average profit P percomputer is given by dividing the total profit P by q: P=100,000q+5,0000.25qdollars. Determine the marginal average profit, dP/dn, at an employee level of 10 engineers. Interpret the result. [HINT: See Example 4.]83E 84E Marginal Revenue The weekly revenue from the sale of rubies at Royal Ruby Retailers is increasing at a rate of $40 per $1 increase in price, and the price is decreasing at a rate of $0.75 per additional ruby sold. What is the marginal revenue? (Be sure to state the units of measurement.) Interpret the result. [HINT: See Quick Example 5.]Marginal Revenue The weekly revenue from the sale of emeralds at Eduardos Emerald Emporium is decreasing at a rate of 500per1 increase in price, and the price is decreasing at a rate of 0.45 peradditional emerald sold. What is the marginal revenue? (Be sure to state the units of measurement.) Interpret the result. [HINT: See Quick Example 5.]87E 88E Existing Home Sales The following graph shows the approximate value of home prices and existing home sales in 20062010 as a percentage change from 2003, together with quadratic approximations: Home prices and sales of existing homes The quadratic approximations are given by Home prices: P(t)=t210t+41(0t4) Existing home sales: S(t)=1.5t211t(0t4), where t is time in years since the start of 2006. Use the chain rule to estimate dSdP|t=2. What does the answer tell you about home sales and prices? [HINT: See Quick Examples 6 and 7.]Existing Home Sales Leading to the Financial Crisis The following graph shows the approximate value of home prices and existing home sales in 20042007 (the 3 years prior to the 2008 economic crisis) as a percentage change from 2003, together with quadratic approximations: Home prices and sales of existing homes The quadratic approximations are given by Home prices: P(t)=6t227t+10(0t3) Existing home sales: S(t)=4t2+4t+11(0t3), where t is time in years since the start of 2004. Use the chain rule to estimate dSdP|t=2. What does the answer tell you about home sales and prices? [HINT: See Quick Examples 6 and 7.]91E 92E 93E 94E Revenue Growth The demand for the Cyberpunk II arcade video game is modeled by the logistic curve q(t)=10,0001+0.5e0.4t, where q(t) is the total number of units sold t months after its introduction. a. Use technology to estimate q(4). b. Assume that the manufacturers of Cyberpunk II sell each unit for 800. What is the companys marginal revenue dR/dq? c. Use the chain rule to estimate the rate at which revenue is growing 4 months after the introduction of the video game.96E Money Stock Exercises 97100 are based on the following demand function for money (taken from a question on the GRE Economics Test): Md=2y0.6r0.3p, Where Md= demand for nominal money balances (money stock y= real income r= an index of interest rates p= an index of prices. These exercises also use the idea of percentage rate of growth: Percentage rate of growth of M =RateofgrowthinMM =dM/dtM. (From the GRE Economics Test) If the interest rate and price level are to remain constant while real income grows at 5% per year, the money stock must grow at what percent per year?98E 99E 100E 101E 102E Say why the following was marked wrong, and give the correct answer. ddx[(3x3x)3]=3(9x21)2 X WRONG!Say why the following was marked wrong, and give the correct answer. ddx[(3x312x2)3]=3(3x212x2)(6x2) X WRONG!105E Name two major errors in the following graded test question, and give the correct answer. ddx[(3x3x)(2x+1)]4=4[(9x21)(2)3] X WRONG SEE ME!107E 108E 109E 110E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=ln(x1)In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=ln(x+3)In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] g(x)=lnx2+3 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] g(x)=ln2x4 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=log2x 6E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=log2(x+1)In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=log3(x2+x)In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] r(t)=log3(t+1/t)In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] r(t)=log3(t+t)In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=ex+3 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=ex2 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=ex2x+1 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=e2x2x+1/x In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] r(x)=(e2x1)2 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] r(x)=(e2x2)3 In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] g(x)=4x In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] g(x)=5x In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=2x21 20E 21E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=(4x2x)lnx In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=(x2+1)5lnx 24E 25E 26E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] g(x)=ln(x22.1x0.3)28E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] g(x)=ln[(2x+1)(x+1)] [HINT: See Example 1(b).]30E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] h(x)=ln(3x+14x2)32E 33E 34E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] s(x)=ln[(4x2)1.3] [HINT: See Example 1 (a).]36E 37E 38E 39E 40E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=ln(x2)[ln(x1)]2 42E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=xex In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f(x)=2exx2ex 45E 46E 47E 48E 49E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] s(x)=e4x1x31 51E In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] v(x)=e2x42x In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] u(x)=3x2x2+1 54E

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