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CalculusFinite Mathematics and Applied Calculus (MindTap Course List)In Exercises 1–10, find d y / d x , using implicit differentiation. In each case, compare your answer with the result obtained by first solving for y as a function of x and then taking the derivative. [ HINT: See Example 1.] x 2 − 2 y = 6BuyFind*arrow_forward*

7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 11.6, Problem 3E

Textbook Problem

In Exercises 1–10, find
* using implicit differentiation. In each case, compare your answer with the result obtained by first solving for y as a function of x and then taking the derivative.* [**HINT:** See Example 1.]

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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In Exercises 41-46, evaluate the given expression....Ch. 11.1 - In Exercises 41-46, evaluate the given expression....Ch. 11.1 - In Exercises 47-52, find the indicated derivative....Ch. 11.1 - In Exercises 47-52, find the indicated derivative....Ch. 11.1 - In Exercises 47-52, find the indicated derivative....Ch. 11.1 - In Exercises 47-52, find the indicated derivative....Ch. 11.1 - In Exercises 47-52, find the indicated derivative....Ch. 11.1 - In Exercises 47-52, find the indicated derivative....Ch. 11.1 - In Exercises 5358, find the slope of the tangent...Ch. 11.1 - In Exercises 5358, find the slope of the tangent...Ch. 11.1 - In Exercises 5358, find the slope of the tangent...Ch. 11.1 - In Exercises 5358, find the slope of the tangent...Ch. 11.1 - In Exercises 5358, find the slope of the tangent...Ch. 11.1 - In Exercises 5358, find the slope of the tangent...Ch. 11.1 - In Exercises 5964, find the equation of the...Ch. 11.1 - In Exercises 5964, find the equation of the...Ch. 11.1 - In Exercises 5964, find the equation of the...Ch. 11.1 - In Exercises 5964, find the equation of the...Ch. 11.1 - In Exercises 5964, find the equation of the...Ch. 11.1 - In Exercises 5964, find the equation of the...Ch. 11.1 - In Exercises 6570, find all values of x (if any)...Ch. 11.1 - In Exercises 6570, find all values of x (if any)...Ch. 11.1 - In Exercises 6570, find all values of x (if any)...Ch. 11.1 - In Exercises 6570, find all values of x (if any)...Ch. 11.1 - In Exercises 6570, find all values of x (if any)...Ch. 11.1 - In Exercises 6570, find all values of x (if any)...Ch. 11.1 - Write out the proof that ddx(x4)=4x3.Ch. 11.1 - Write out the proof that ddx(x5)=5x4Ch. 11.1 - If Exercises 73-76, determine whether f is...Ch. 11.1 - If Exercises 73-76, determine whether f is...Ch. 11.1 - If Exercises 73-76, determine whether f is...Ch. 11.1 - If Exercises 73-76, determine whether f is...Ch. 11.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 11.1 - In Exercises 77-88, say whether lHospitals rule...Ch. 11.1 - In Exercises 77-88, say whether lHospitals rule...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. How do the derivatives of f...Ch. 11.1 - Following is an excerpt from your best friends...Ch. 11.1 - Following is an excerpt from your own graded...Ch. 11.1 - Following is an excerpt from your best friends...Ch. 11.1 - Following is an excerpt from your second best...Ch. 11.1 - Following is an excerpt from your second best...Ch. 11.1 - Following is an excerpt from your second enemys...Ch. 11.1 - One of the questions in your last calculus test...Ch. 11.1 - How would you respond to an acquaintance who says,...Ch. 11.1 - Sketch the graph of a function whose derivative is...Ch. 11.1 - Sketch the graph of a function that has a tangent...Ch. 11.2 - In Exercises 14, for each cost function, find the...Ch. 11.2 - In Exercises 14, for each cost function, find the...Ch. 11.2 - In Exercises 14, for each cost function, find the...Ch. 11.2 - In Exercises 14, for each cost function, find the...Ch. 11.2 - In Exercises 5 and 6, find the marginal cost,...Ch. 11.2 - In Exercises 5 and 6, find the marginal cost,...Ch. 11.2 - A certain cost function has the following graph:...Ch. 11.2 - A certain cost function has the following graph:...Ch. 11.2 - Advertising Costs The cost, in thousands of...Ch. 11.2 - Marginal Cost and Average Cost The cost of...Ch. 11.2 - Marginal and Average Cost: iPhones Assume that it...Ch. 11.2 - Marginal and Average Cost: PlayStation 4s Assume...Ch. 11.2 - Marginal Revenue and Profit Your college...Ch. 11.2 - Marginal Revenue and Profit The Audubon Society at...Ch. 11.2 - Marginal Profit Suppose P(x) represents the profit...Ch. 11.2 - Marginal Loss An automobile retailer calculates...Ch. 11.2 - Marginal Profit Your monthly profit (in dollars)...Ch. 11.2 - Marginal Profit Your monthly profit (in dollars)...Ch. 11.2 - Marginal Revenue: Pricing Tuna Assume that the...Ch. 11.2 - Marginal Revenue: Pricing Tuna Repeat Exercise 19,...Ch. 11.2 - Marginal Product A car wash firm calculates that...Ch. 11.2 - Marginal Product Repeat Exercise 21 using the...Ch. 11.2 - Average and Marginal Cost The daily cost to...Ch. 11.2 - Average and Marginal Cost Repeat Exercise 23,...Ch. 11.2 - Advertising Cost Your company is planning to air a...Ch. 11.2 - Housing Costs The cost C of building a house is...Ch. 11.2 - Emission Control The cost of controlling emissions...Ch. 11.2 - Taxation Schemes To raise revenues during the...Ch. 11.2 - Fuel Economy Your Porsches gas mileage (in miles...Ch. 11.2 - Marginal Revenue The estimated marginal revenue...Ch. 11.2 - Marginal Cost (from the GRE Economics Test) In a...Ch. 11.2 - Study Time (from the GRE economics test) A student...Ch. 11.2 - Marginal Product (from the GRE Economics Test)...Ch. 11.2 - Marginal Product (based on a question from the GRE...Ch. 11.2 - The marginal cost of producing the 1,001st item is...Ch. 11.2 - For the cost function C(x)=mx+b themarginal cost...Ch. 11.2 - What is a cost function? 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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You need not...Ch. 11.3 - In Exercises 57-62, compute the indicated...Ch. 11.3 - In Exercises 57-62, compute the indicated...Ch. 11.3 - In Exercises 57-62, compute the indicated...Ch. 11.3 - In Exercises 57-62, compute the indicated...Ch. 11.3 - In Exercises 57-62, compute the indicated...Ch. 11.3 - In Exercises 57-62, compute the indicated...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...Ch. 11.3 - In Exercises 63-70, use the calculation thought...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 - 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 - 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 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...Ch. 11.4 - In Exercises 1-50, calculate the derivate of the...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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Explain why one should not expect dy/dx tobe a...Ch. 11.6 - If y is a function of x and dy/dx0 atsome point,...Ch. 11.6 - If you are given an equation in x and y such that...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - In Exercises 1-32, find the derivative of the...Ch. 11 - 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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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