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Math Calculus Calculus & Its Applications (14th Edition)

The value of g ( x ) , where f ( x ) and g ( x ) are differentiable functions, and d d x f ( g ( x ) ) = 3 x 2 ⋅ f ' ( x 3 + 1 ) .

The value of g ( x ) , where f ( x ) and g ( x ) are differentiable functions, and d d x f ( g ( x ) ) = 3 x 2 ⋅ f ' ( x 3 + 1 ) .

Solution Summary: The author explains that g(x)=x3+1 are differentiable functions.

Calculus & Its Applications (14th Edition)

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 3.2, Problem 57E

To determine

The value of g(x), where f(x) and g(x) are differentiable functions, and ddxf(g(x))=3x2⋅f'(x3+1).

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Chapter 3.2, Problem 56E

Chapter 3.2, Problem 58E

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Differentiate the function G(x) = 7x-7 + 5x-9. Answer G'(x) =

Chapter 3 Solutions

Calculus & Its Applications (14th Edition)

Ch. 3.1 - Consider the function y=(x+1)x. Differentiate y by...Ch. 3.1 - Prob. 2CYU Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28. y=xx Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28. y=[...

Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Prob. 18E Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28. y=[...Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Differentiate the functions in Exercise 1-28....Ch. 3.1 - Find the equation of the tangent line to the curve...Ch. 3.1 - Find the equation of the tangent line to the curve...Ch. 3.1 - Find all x-coordinates of points (x,y) on the...Ch. 3.1 - Find the inflection points on the graph of...Ch. 3.1 - Find all x such that dydx=0, where...Ch. 3.1 - The graph of y=(x21)4(x2+1)5 is shown in Fig. 3....Ch. 3.1 - Find the point(s) on the graph of y=(x2+3x1)/x...Ch. 3.1 - Find the point(s) on the graph of y=(2x4+1)(x5)...Ch. 3.1 - Find d2ydx2. y=(x2+1)4 Ch. 3.1 - Find d2ydx2. y=x2+1 Ch. 3.1 - Find d2ydx2 y=xx+1 Ch. 3.1 - Find d2ydx2 y=22+x2 Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - In Exercises 4144, a function h(x) is defined in...Ch. 3.1 - Volume An open rectangular box is 3 feet long and...Ch. 3.1 - Volume A closed rectangular box is to be...Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Average Revenue Let R(x) be the revenue received...Ch. 3.1 - Average Velocity Let s(t) be the number of miles a...Ch. 3.1 - Prob. 51E Ch. 3.1 - Cost-Benefit of Emission Control A manufacturer...Ch. 3.1 - In Exercises 53 and 54, use the fact that at the...Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - If f(x) and g(x) are differentiable functions such...Ch. 3.1 - If f(x) and g(x) are differentiable functions such...Ch. 3.1 - Prob. 62E Ch. 3.1 - Let f(x)=1/x and g(x)=x3. Show that the product...Ch. 3.1 - Prob. 64E Ch. 3.1 - Prob. 65E Ch. 3.1 - Prob. 66E Ch. 3.1 - Prob. 67E Ch. 3.1 - Prob. 68E Ch. 3.1 - Prob. 69E Ch. 3.2 - Consider the function h(x)=(2x35)5+(2x35)4 Write...Ch. 3.2 - Consider the function h(x)=(2x35)5+(2x35)4 Compute...Ch. 3.2 - Prob. 3CYU Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Compute f(g(x)), where f(x) and g(x) are the...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Each of following functions may be viewed as a...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - Differentiate the functions in Exercises 1120...Ch. 3.2 - In Exercises 2126, a function h(x) is defined in...Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - In Exercises 2126, a function h(x) is defined in...Ch. 3.2 - In Exercises 2126, a function h(x) is defined in...Ch. 3.2 - Prob. 26E Ch. 3.2 - Sketch the graph of y=4x/(x+1)2,x1.Ch. 3.2 - Sketch the graph of y=2/(1+x2)Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute ddxf(g(x)), where f(x) and g(x) are...Ch. 3.2 - Compute dydx using the chain rule in formula (1)....Ch. 3.2 - Compute dydx using the chain rule in formula (1)....Ch. 3.2 - Compute dydx using the chain rule in formula (1)....Ch. 3.2 - Compute dydxt=t0 y=x23x,x=t2+3,t0=0 Ch. 3.2 - Compute dydxt=t0 y=(x22x+4)2,x=1t+1,t0=1 Ch. 3.2 - Compute dydxt=t0 y=x+1x1,x=t24,t0=3 Ch. 3.2 - Prob. 44E Ch. 3.2 - Find the equation of the line tangent to the graph...Ch. 3.2 - Find the equation of the line tangent to the graph...Ch. 3.2 - Find the x- coordinate of all points on the curve...Ch. 3.2 - The function f(x)=x26x+10 has one relative minimum...Ch. 3.2 - Prob. 49E Ch. 3.2 - Allometric Equation Many relations in biology are...Ch. 3.2 - Suppose that P, y and t are variables, where P is...Ch. 3.2 - Suppose that Q, x and y are variables, where Q is...Ch. 3.2 - Marginal Profit and Times Rate of Change When a...Ch. 3.2 - Marginal Cost and Time Rate of Change The cost of...Ch. 3.2 - A model for Carbon Monoxide Levels Ecologists...Ch. 3.2 - Profit A manufacturer of microcomputers estimates...Ch. 3.2 - Prob. 57E Ch. 3.2 - Prob. 58E Ch. 3.2 - If f(x) and g(x) are differentiable functions,...Ch. 3.2 - Prob. 60E Ch. 3.2 - Effect of Stocks on Total Assets of a Company...Ch. 3.2 - Refer to Exercise 61. Use chain rule to find...Ch. 3.2 - Refer to Exercise 61. Find dxdt|t=2.5 and...Ch. 3.2 - Refer to Exercise 61. What was the maximum value...Ch. 3.2 - In an expression of the form f(g(x)), f(x) is...Ch. 3.3 - Solution can be found following the section...Ch. 3.3 - Solution can be found following the section...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - In Exercise 1-18, suppose that x and y are related...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Use implicit differentiation of the equation in...Ch. 3.3 - Find the equation of the tangent line to the graph...Ch. 3.3 - Find the equation of the tangent line to the graph...Ch. 3.3 - Slope of the Lemniscate The graph of...Ch. 3.3 - The graph of x4+2x2y2+y4=9x29y2 is a lemniscate...Ch. 3.3 - Marginal Rate of Substitution Suppose that x and y...Ch. 3.3 - Demand Equation Suppose that x and y represents...Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - Prob. 34E Ch. 3.3 - In Exercise 31 36, suppose that x and y are both...Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Demand Equation Suppose that the price p (in...Ch. 3.3 - Demand Equation Suppose that the price p (in...Ch. 3.3 - Advertising Affects Revenue The monthly...Ch. 3.3 - Rate of Change of Price Suppose that in Boston the...Ch. 3.3 - Related Rates Figure 7 shows a 10- foot ladder...Ch. 3.3 - Related Rates An airplane flying 390 feet per...Ch. 3.3 - Related Rates A baseball diamond is a 90- foot by...Ch. 3.3 - Related Rates A motorcyclist is driving over a...Ch. 3 - State the product rule and quotient rule.Ch. 3 - Prob. 2CCE Ch. 3 - Prob. 3CCE Ch. 3 - Prob. 4CCE Ch. 3 - Prob. 5CCE Ch. 3 - Prob. 6CCE Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions. y=x(x51)3 Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions. y=xx+4 Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions....Ch. 3 - Differentiate the following functions. y=x26xx2 Ch. 3 - Differentiate the following functions. y=2x23x Ch. 3 - Differentiate the following functions. y=(3x2x3)2 Ch. 3 - Differentiate the following functions. y=x3+xx2x Ch. 3 - Let f(x)=(3x+1)4(3x)5. Find all x such that...Ch. 3 - Let f(x)=x2+1x2+5. Find all x such that f(x)=0.Ch. 3 - Find the equation of the line tangent to the graph...Ch. 3 - Find the equation of the line tangent to the graph...Ch. 3 - Minimizing Area A botanical display is to be...Ch. 3 - Repeat Exercise 17, with the sidewalk on the...Ch. 3 - Cost function A store estimates that its cost when...Ch. 3 - Rate of Change of Taxes A company pays y dollars...Ch. 3 - In Exercise 21-23, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 21-23, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 21-23, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 24-26, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 24-26, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 24-26, find a formula for ddxf(g(x)),...Ch. 3 - In Exercise 27-29, find dydx, where y is a...Ch. 3 - In Exercise 27-29, find dydx, where y is a...Ch. 3 - In Exercise 27-29, find dydx, where y is a...Ch. 3 - In Exercises 30 32, find dydx, where y is a...Ch. 3 - In Exercises 30 32, find dydx, where y is a...Ch. 3 - In Exercises 30 32, find dydx, where y is a...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Exercises 33 38 refer to the graphs of the...Ch. 3 - Revenue Function The revenue, R, that a company...Ch. 3 - Amount of Drug Usage The amount, A, of anesthetics...Ch. 3 - The graph of x2/3+y2/3=8 is the astroid in Fig. 3...Ch. 3 - Slope of the Folium of Descartes The graph of...Ch. 3 - Slope of the Folium of Descartes The graph of...Ch. 3 - In Exercises 43-46, x and y are related by the...Ch. 3 - In Exercises 43-46, x and y are related by the...Ch. 3 - In Exercises 43-46, x and y are related by the...Ch. 3 - Cost Analysis and Production A factorys weekly...Ch. 3 - Use of Books at a Library A town library estimates...Ch. 3 - Demand equation Suppose that the price p and...Ch. 3 - Volume of an Oil Spill An offshore oil well is...Ch. 3 - Weight and Surface Area Animal physiologists have...Ch. 3 - Sales and Advertising Suppose that a kitchen...

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