Math

CalculusFinite Mathematics and Applied Calculus (MindTap Course List)In Exercises 1–12 (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 ) = x ⋅ x 2BuyFind*arrow_forward*

7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 11.3, Problem 3E

Textbook Problem

In Exercises 1–12

*(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.]

Finite Mathematics and Applied Calculus (MindTap Course List)

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Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...Ch. 11.1 - In Exercises 1-10, use the shortcut rules to...

Ch. 11.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 11.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 11.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 11.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 11.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 11.1 - In Exercises 11-16, obtain the derivative dy/dt...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - In Exercises 17-40, find the derivative of the...Ch. 11.1 - 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GE Net Income 2009-2013 The annual net income of...Ch. 11.1 - GE Net Income 20072011 The annual net income of...Ch. 11.1 - Ecology Increasing numbers of manatees (sea...Ch. 11.1 - SAT Scores by Income The following graph shown...Ch. 11.1 - Market Share: Smartphones The following graph...Ch. 11.1 - Market Share: Smartphones The following graph...Ch. 11.1 - What instructions would you give to a fellow...Ch. 11.1 - What instructions would you give to a fellow...Ch. 11.1 - Consider f(x)=x2 and g(x)=2x2 =. How do the slopes...Ch. 11.1 - Consider f(x)=x3 and g(x)=x3+3. How do the slopes...Ch. 11.1 - Suppose g(x)=f(x). How do the derivatives of f and...Ch. 11.1 - Suppose g(x)=f(x)50. 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Carefully explain the...Ch. 11.2 - The cost function for your grand piano...Ch. 11.2 - Give an example of a cost function for which the...Ch. 11.2 - Give an example of a cost function for which the...Ch. 11.2 - If the average cost to manufacture one grand piano...Ch. 11.2 - If your analysis of a manufacturing company...Ch. 11.2 - If the marginal cost is decreasing, is the average...Ch. 11.2 - If the average cost is decreasing, is the marginal...Ch. 11.2 - If a companys marginal average cost is zero at the...Ch. 11.2 - The acceleration of cost is defined as the...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 112 (a) Calculate the derivative of...Ch. 11.3 - In Exercises 13-28, calculate dydx. 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In Exercises 71-76, find the equation of the line...Ch. 11.3 - In Exercises 71-76, find the equation of the line...Ch. 11.3 - In Exercises 71-76, find the equation of the line...Ch. 11.3 - Revenue The monthly sales of Sunny Electronics new...Ch. 11.3 - Revenue The monthly sales of Sunny Electronics new...Ch. 11.3 - Saudi Oil Revenues The price of crude oil during...Ch. 11.3 - Russian Oil Revenues The price of crude oil during...Ch. 11.3 - Revenue Dorothy Wagner is currently selling 20 I ...Ch. 11.3 - Pricing Policy Let us turn Exercise 81 around a...Ch. 11.3 - Bus Travel Thoroughbred Bus Company finds that its...Ch. 11.3 - Bus Travel Thoroughbred Bus Company finds that its...Ch. 11.3 - Fuel Economy Your muscle cars gas mileage (in...Ch. 11.3 - Fuel Economy Your used Chevys gas mileage (in...Ch. 11.3 - Oil Imports from Mexico Daily oil production in...Ch. 11.3 - Oil Imports from Mexico Daily oil production in...Ch. 11.3 - Military Spending The annual cost per active-duty...Ch. 11.3 - Military Spending in the 1990s The annual cost per...Ch. 11.3 - Biology-Reproduction The Verhulst model for...Ch. 11.3 - Biology-Reproduction Another model, the predator...Ch. 11.3 - Embryo Development Bird embryos consume oxygen...Ch. 11.3 - Embryo Developmen Turkey embryos consume oxy- gen...Ch. 11.3 - If f and g are functions of time, and at time t=3,...Ch. 11.3 - If f and g are functions of time, and at time t=2,...Ch. 11.3 - If f and g are functions of time, and at time t=3,...Ch. 11.3 - If f and g are functions of time, and at time t=2,...Ch. 11.3 - You have come across the following in a newspaper...Ch. 11.3 - Your friend says that because average cost is...Ch. 11.3 - Find a demand function q(p) suchthat, at a price...Ch. 11.3 - What must be true about a demand function q(p)...Ch. 11.3 - You and I are both selling a steady 20 T-shirts...Ch. 11.3 - You and I are both selling T-shirts for a steady...Ch. 11.3 - Marginal Product (from the GRE Economics Test)...Ch. 11.3 - Marginal Cost (based on a question from the GRE...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - 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The...Ch. 11.4 - Food versus Education The percentage y (of total...Ch. 11.4 - Food versus Recreation The percentage y (of total...Ch. 11.4 - Marginal Revenue The weekly revenue from the sale...Ch. 11.4 - Marginal Revenue The weekly revenue from the sale...Ch. 11.4 - Crime Statistics The murder rate in large cities...Ch. 11.4 - Crime Statistics Following is a quadratic model...Ch. 11.4 - Existing Home Sales The following graph shows the...Ch. 11.4 - Existing Home Sales Leading to the Financial...Ch. 11.4 - Pollution An offshore oil well is leaking oil and...Ch. 11.4 - Mold A mold culture in a dorm refrigerator is...Ch. 11.4 - Budget Overruns The Pentagon is planning to build...Ch. 11.4 - Soap Bubbles The soap bubble I am blowing has a...Ch. 11.4 - Revenue Growth The demand for the Cyberpunk II...Ch. 11.4 - Information Highway The amount of information...Ch. 11.4 - Money Stock Exercises 97100 are based on the...Ch. 11.4 - Money Stock Exercises 97100 are based on the...Ch. 11.4 - Money Stock Exercises 97100 are based on the...Ch. 11.4 - Money Stock Exercises 97100 are based on the...Ch. 11.4 - Complete the following: The derivative of 1 over a...Ch. 11.4 - Complete the following: The derivative of the...Ch. 11.4 - Say why the following was marked wrong, and give...Ch. 11.4 - Say why the following was marked wrong, and give...Ch. 11.4 - Name two major errors in the following graded test...Ch. 11.4 - Name two major errors in the following graded test...Ch. 11.4 - Formulate a simple procedure for deciding whether...Ch. 11.4 - Give an example of a function f with the property...Ch. 11.4 - Give an example of a function f with the property...Ch. 11.4 - What can you say about the composite of two linear...Ch. 11.5 - In Exercises 1-66, find the derivative of the...Ch. 11.5 - In Exercises 1-66, find the derivative of the...Ch. 11.5 - In Exercises 1-66, find the derivative of the...Ch. 11.5 - In Exercises 1-66, find the derivative of the...Ch. 11.5 - In Exercises 1-66, find the derivative of the...Ch. 11.5 - In Exercises 1-66, find the derivative of the...Ch. 11.5 - 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Investments If $20,000 is invested in a savings...Ch. 11.5 - The 2003 SARS Outbreak In the early stages of the...Ch. 11.5 - The 2003 SARS Outbreak A few weeks into the deadly...Ch. 11.5 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 11.5 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 11.5 - SAT Scores by Income The following bar graph shows...Ch. 11.5 - SAT Scores by Income The following bar graph shows...Ch. 11.5 - Demographics: Average Age and Fertility The...Ch. 11.5 - Demographics: Average Age and Fertility The...Ch. 11.5 - Epidemics A flu epidemic described in Example 1 in...Ch. 11.5 - Epidemics Another epidemic follows the curve...Ch. 11.5 - Subprime Mortgages during the Housing Bubble...Ch. 11.5 - Subprime Mortgage Debt during the Housing Bubble...Ch. 11.5 - Subprime Mortgages during the Housing Bubble...Ch. 11.5 - Subprime Mortgage Debt during the Housing Bubble...Ch. 11.5 - Population Growth The population of Lower Anchovia...Ch. 11.5 - Population Growth The population of Upper Anchovia...Ch. 11.5 - Radioactive Decay Plutonium 239 has a half-life of...Ch. 11.5 - Radioactive Decay Carbon 14 has a half-life of...Ch. 11.5 - Cellphone Revenues The number of cellphone...Ch. 11.5 - Cellphone Revenues The annual revenue for...Ch. 11.5 - Complete the following: The derivative of e raised...Ch. 11.5 - Complete the following: The derivative of the...Ch. 11.5 - Complete the following: The derivative of 2 raised...Ch. 11.5 - Complete the following: The derivative of the base...Ch. 11.5 - What is wrong with the following?...Ch. 11.5 - What is wrong with the following? ddx22x=(2)22x X...Ch. 11.5 - What is wrong with the following? ddx32x=(2x)32x1...Ch. 11.5 - What is wrong with the following? ddxln(3x21)=16x...Ch. 11.5 - The number N of music downloads on campus is...Ch. 11.5 - The number N of graphing calculators sold on...Ch. 11.5 - Show that the fractional rate of change of the...Ch. 11.5 - Show that the fractional rate of change of f(x) is...Ch. 11.5 - Let A(t) representa quantity growing...Ch. 11.5 - 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Jay Campbell, who...Ch. 11 - Percentage Rate of Change of P/E Ratios Refer to...Ch. 11 - Sales OHaganBooks.com decided that the cubic curve...Ch. 11 - Rising Sea Level Upon some reflection, Marjory...Ch. 11 - Website Activity The number of hits on...Ch. 11 - Website Activity The number of hits on...Ch. 11 - Demand and Revenue The price p that...Ch. 11 - Demand and Revenue The price p that...Ch. 11 - Find limt+N(t) forboth models, and interpret the...

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