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Math Calculus Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

(a) Use the Product Rule twice to prove that if f, g, and h are differentiable, then ( fgh ) ' = f'gh + fg'h + fgh'. (b) Taking f = g = h in part (a), show that d x [ f ( x ) ] 3 = 3 [ f ( x ) ] 2 f ' ( x ) (c) Use part (b) to differentiate y = e 3 x .

(a) Use the Product Rule twice to prove that if f, g, and h are differentiable, then ( fgh ) ' = f'gh + fg'h + fgh'. (b) Taking f = g = h in part (a), show that d x [ f ( x ) ] 3 = 3 [ f ( x ) ] 2 f ' ( x ) (c) Use part (b) to differentiate y = e 3 x .

Solution Summary: The author illustrates how the derivative of p=fg is computed as follows: Apply the product rule and simplify.

Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

18th Edition

ISBN: 9780357008034

Author: Stewart

Publisher: CENGAGE L

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Textbook Question

Chapter 3.2, Problem 61E

(a) Use the Product Rule twice to prove that if f, g, and h are differentiable, then (fgh)' = f'gh + fg'h + fgh'.

(b) Taking f = g = h in part (a), show that

d x [ f ( x ) ] 3 = 3 [ f ( x ) ] 2 f ' ( x )

(c) Use part (b) to differentiate y = e^3x.

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Chapter 3.2, Problem 60E

Chapter 3.2, Problem 62E

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Chapter 3 Solutions

Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

Ch. 3.1 - (a) How is the number e defined? (b) Use a...Ch. 3.1 - Prob. 2E Ch. 3.1 - Differentiate the function. f(x) = 240 Ch. 3.1 - Differentiate the function. f(x) = e5 Ch. 3.1 - Differentiate the function. f(x) = 5.2x + 2.3 Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Differentiate the function. f(t) = 1.4t5 2.5t2+...Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Differentiate the function. B(y) = cy6 Ch. 3.1 - Prob. 13E Ch. 3.1 - Differentiate the function. y = x5/3 x2/3 Ch. 3.1 - Differentiate the function. R(a) = (3a + 1)2 Ch. 3.1 - Differentiate the function. h(t)=t44et Ch. 3.1 - Differentiate the function. S(p)=pp Ch. 3.1 - Differentiate the function. y=x3(2+x)Ch. 3.1 - Differentiate the function. y=3ex+4x3 Ch. 3.1 - Differentiate the function. S(R) = 4R2 Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Differentiate the function. D(t)=1+16t2(4t)3 Ch. 3.1 - Prob. 31E Ch. 3.1 - Differentiate the function. y = ex + 1 + 1 Ch. 3.1 - Prob. 33E Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Find an equation of the tangent line to the curve...Ch. 3.1 - Prob. 36E Ch. 3.1 - Find equations of the tangent line and normal line...Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Find the points on the curve y = 2x3 + 3x2 12x +...Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - Prob. 61E Ch. 3.1 - Where does the normal line to the parabola y = x2 ...Ch. 3.1 - Draw a diagram to show that there are two tangent...Ch. 3.1 - Prob. 64E Ch. 3.1 - Prob. 65E Ch. 3.1 - Find the nth derivative of each function by...Ch. 3.1 - Prob. 67E Ch. 3.1 - The equation y" + y' 2y = x2 is called a...Ch. 3.1 - Find a cubic function y = ax3 + bx2 + cx + d whose...Ch. 3.1 - Prob. 70E Ch. 3.1 - Prob. 71E Ch. 3.1 - At what numbers is the following function g...Ch. 3.1 - Prob. 73E Ch. 3.1 - Prob. 74E Ch. 3.1 - Find the parabola with equation y = ax2 + bx whose...Ch. 3.1 - Prob. 76E Ch. 3.1 - Prob. 77E Ch. 3.1 - Prob. 78E Ch. 3.1 - What is the value of c such that the line y = 2x +...Ch. 3.1 - Prob. 80E Ch. 3.1 - Prob. 81E Ch. 3.1 - A tangent line is drawn to the hyperbola xy = c at...Ch. 3.1 - Prob. 83E Ch. 3.1 - Prob. 84E Ch. 3.1 - Prob. 85E Ch. 3.1 - Prob. 86E Ch. 3.2 - Find the derivative of f(x) = (1 + 2x2)(x x2) in...Ch. 3.2 - Find the derivative o f the function...Ch. 3.2 - Prob. 3E Ch. 3.2 - Differentiate. g(x)=(x+22)ex Ch. 3.2 - Differentiate. y=xex Ch. 3.2 - Differentiate. y=ex1ex Ch. 3.2 - Prob. 7E Ch. 3.2 - Differentiate. G(x)=x222x+1 Ch. 3.2 - Differentiate. H(u)=(uu)(u+u)Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Differentiate. F(t)=AtBt2+Ct3 Ch. 3.2 - Prob. 25E Ch. 3.2 - Differentiate. f(x)=ax+bcx+d Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Find equations of the tangent line and normal line...Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - If h(2) = 4 and h'(2) = 3, find ddx(h(x)x)|x=2 Ch. 3.2 - Prob. 47E Ch. 3.2 - Prob. 48E Ch. 3.2 - If f and g are the functions whose graphs are...Ch. 3.2 - Prob. 50E Ch. 3.2 - Prob. 51E Ch. 3.2 - If f is a differentiable function, find an...Ch. 3.2 - Prob. 53E Ch. 3.2 - Find equations of the tangent lines to the curve...Ch. 3.2 - Prob. 55E Ch. 3.2 - Prob. 56E Ch. 3.2 - Prob. 57E Ch. 3.2 - A manufacturer produces bolts of a fabric with a...Ch. 3.2 - Prob. 59E Ch. 3.2 - The biomass B(t) of a fish population is the total...Ch. 3.2 - (a) Use the Product Rule twice to prove that if f,...Ch. 3.2 - (a) If F(x) = f(x) g(x), where f and g have...Ch. 3.2 - Find expressions for the first five derivatives of...Ch. 3.2 - Prob. 64E Ch. 3.3 - Prob. 1E Ch. 3.3 - Differentiate. f(x) = x cos x + 2 tan x Ch. 3.3 - Differentiate. f(x) = ex cos x Ch. 3.3 - Differentiate. y = 2 sec x csc x Ch. 3.3 - Differentiate. y = sec tan Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Differentiate f()=sin1+cos Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Differentiate. y=sint1+tant Ch. 3.3 - Differentiate. f() = cos sin Ch. 3.3 - Differentiate. f(t) = tet cot t Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prove, using the definition of derivative. that if...Ch. 3.3 - Prob. 21E Ch. 3.3 - Find an equation of the tangent line to the curve...Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - If H() = sin , find H'() and H"( ).Ch. 3.3 - If f(t) = sec t, find f"(/4).Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - For what values of x does the graph of f have a...Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - An elastic band is hung on a hook and a mass is...Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Prob. 47E Ch. 3.3 - Prob. 48E Ch. 3.3 - Prob. 49E Ch. 3.3 - Prob. 50E Ch. 3.3 - Find the given derivative by finding the first few...Ch. 3.3 - Find the given derivative by finding the first few...Ch. 3.3 - Prob. 53E Ch. 3.3 - Prob. 54E Ch. 3.3 - Differentiate each trigonometric identity to...Ch. 3.3 - A semicircle with diameter PQ sits on an isosceles...Ch. 3.3 - The figure shows a circular arc of length s and a...Ch. 3.3 - Prob. 58E Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Prob. 3E Ch. 3.4 - Write the composite function in the form f(g(x))....Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Find the derivative of the function. F(x) = (5x6 +...Ch. 3.4 - Find the derivative of the function. F (x) = (1 +...Ch. 3.4 - Find the derivative of the function. f(x)=5x+1 Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Prob. 13E Ch. 3.4 - Find the derivative of the function. f(t) = t sin ...Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Find the derivative of the function. f(x) = (2x ...Ch. 3.4 - Find the derivative of the function. g(x) = (x2 +...Ch. 3.4 - Prob. 19E Ch. 3.4 - Find the derivative of the function. F(t) = (3t ...Ch. 3.4 - Prob. 21E Ch. 3.4 - Find the derivative of the function. y=(x+1x)5 Ch. 3.4 - Prob. 23E Ch. 3.4 - Find the derivative of the function. f(t)2t3 Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Prob. 27E Ch. 3.4 - Find the derivative of the function. f(z) =...Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Find the derivative of the function. y = x2 e1/x Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Find the derivative of the function. g(x) = (2...Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Find y and y. y=eex Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Find an equation of the tangent line to the curve...Ch. 3.4 - Prob. 53E Ch. 3.4 - Prob. 54E Ch. 3.4 - Prob. 55E Ch. 3.4 - Prob. 56E Ch. 3.4 - Prob. 57E Ch. 3.4 - Prob. 58E Ch. 3.4 - Prob. 59E Ch. 3.4 - At what point on the curve y=1+2x is the tangent...Ch. 3.4 - Prob. 61E Ch. 3.4 - Prob. 62E Ch. 3.4 - A table of values for f, g, f, and g is given. (a)...Ch. 3.4 - Let f and g be the functions in Exercise 63. (a)...Ch. 3.4 - Prob. 65E Ch. 3.4 - Prob. 66E Ch. 3.4 - Prob. 67E Ch. 3.4 - Suppose f is differentiable on and is a real...Ch. 3.4 - Suppose f is differentiable on . Let F(x) = f(ex)...Ch. 3.4 - Prob. 70E Ch. 3.4 - Prob. 71E Ch. 3.4 - Prob. 72E Ch. 3.4 - Prob. 73E Ch. 3.4 - Prob. 74E Ch. 3.4 - Prob. 75E Ch. 3.4 - Prob. 76E Ch. 3.4 - Prob. 77E Ch. 3.4 - Find the 1000th derivative of f(x) = xex.Ch. 3.4 - The displacement of a particle on a vibrating...Ch. 3.4 - If the equation of motion of a particle is given...Ch. 3.4 - Prob. 81E Ch. 3.4 - Prob. 82E Ch. 3.4 - The motion of a spring that is subject to a...Ch. 3.4 - Prob. 84E Ch. 3.4 - The average blood alcohol concentration (BAC) of...Ch. 3.4 - In Section 1.4 we modeled the world population...Ch. 3.4 - Prob. 87E Ch. 3.4 - Prob. 88E Ch. 3.4 - Prob. 89E Ch. 3.4 - The table gives the US population from 1790 to...Ch. 3.4 - Prob. 93E Ch. 3.4 - Prob. 94E Ch. 3.4 - (a) If n is a positive integer, prove that...Ch. 3.4 - Prob. 96E Ch. 3.4 - Prob. 97E Ch. 3.4 - Prob. 98E Ch. 3.4 - Prob. 99E Ch. 3.4 - If y = f(u) and u = g(x), where f and g possess...Ch. 3.5 - (a) Find y by implicit differentiation. (b) Solve...Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Find dy/dx by implicit differentiation. 5. x2 4xy...Ch. 3.5 - Prob. 6E Ch. 3.5 - Find dy/dx by implicit differentiation. 7. x4 +...Ch. 3.5 - Find dy/dx by implicit differentiation. 8. x3 xy2...Ch. 3.5 - Find dy/dx by implicit differentiation. 9....Ch. 3.5 - Find dy/dx by implicit differentiation. 10. xey =...Ch. 3.5 - Find dy/dx by implicit differentiation. 11. y cos...Ch. 3.5 - Find dy/dx by implicit differentiation. 12....Ch. 3.5 - Find dy/dx by implicit differentiation. 13....Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Find dy/dx by implicit differentiation. 19....Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Regard y as the independent variable and x as the...Ch. 3.5 - Regard y as the independent variable and x as the...Ch. 3.5 - Prob. 25E Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Prob. 27E Ch. 3.5 - Prob. 28E Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Prob. 30E Ch. 3.5 - Use implicit differentiation to find an equation...Ch. 3.5 - Prob. 32E Ch. 3.5 - (a) The curve with equation y2 = 5x4 x2 is called...Ch. 3.5 - Prob. 34E Ch. 3.5 - Find y by implicit differentiation. 35. x2 + 4y2 =...Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - If x2 + xy + y3 = 1, find the value of y at the...Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Find an equation of the tangent line to the...Ch. 3.5 - Prob. 46E Ch. 3.5 - Show, using implicit differentiation, that any...Ch. 3.5 - Prob. 48E Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Prob. 52E Ch. 3.5 - Prob. 53E Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Prob. 55E Ch. 3.5 - Prob. 56E Ch. 3.5 - Find the derivative of the function. Simplify...Ch. 3.5 - Prob. 58E Ch. 3.5 - Prob. 59E Ch. 3.5 - Prob. 60E Ch. 3.5 - Prob. 61E Ch. 3.5 - Prob. 62E Ch. 3.5 - Prove the formula for (d/dx)(cos1x) by the same...Ch. 3.5 - (a) One way of defining sec1x is to say that...Ch. 3.5 - Prob. 65E Ch. 3.5 - Prob. 66E Ch. 3.5 - Prob. 67E Ch. 3.5 - Two curves are orthogonal if their tangent lines...Ch. 3.5 - Show that the ellipse x2/a2 + y2/b2 = 1 and the...Ch. 3.5 - Prob. 70E Ch. 3.5 - Prob. 71E Ch. 3.5 - Prob. 73E Ch. 3.5 - (a) Where does the normal line to the ellipse x2 ...Ch. 3.5 - Prob. 75E Ch. 3.5 - Prob. 76E Ch. 3.5 - Prob. 77E Ch. 3.5 - Prob. 78E Ch. 3.5 - The Bessel function of order 0, y = J(x),...Ch. 3.5 - The figure shows a lamp located three units to the...Ch. 3.6 - Explain why the natural logarithmic function y =...Ch. 3.6 - Differentiate the function. f(x) = x ln x x Ch. 3.6 - Differentiate the function. f(x ) = sin(ln x)Ch. 3.6 - Differentiate the function. f(x) = ln(sin2x)Ch. 3.6 - Differentiate the function. f(x)=ln1x Ch. 3.6 - Differentiate the function. y=1lnx Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Differentiate the function. F(t) =(ln t)2 sin t Ch. 3.6 - Differentiate the function. h(x)=ln(x+x21)Ch. 3.6 - Differentiate the function. G(y)=ln(2y+1)5y2+1 Ch. 3.6 - Prob. 14E Ch. 3.6 - Differentiate the function. F(s) = ln ln s Ch. 3.6 - Differentiate the function. y = ln |1 + t t3|Ch. 3.6 - Differentiate the function. T(z) = 2z log2z Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 19E Ch. 3.6 - Differentiate the function. H(z)=a2z2a2+z2 Ch. 3.6 - Prob. 21E Ch. 3.6 - Prob. 22E Ch. 3.6 - Prob. 23E Ch. 3.6 - Find y and y. y=lnx1+lnx Ch. 3.6 - Prob. 25E Ch. 3.6 - Prob. 26E Ch. 3.6 - Prob. 27E Ch. 3.6 - Prob. 28E Ch. 3.6 - Prob. 29E Ch. 3.6 - Prob. 30E Ch. 3.6 - Prob. 31E Ch. 3.6 - Prob. 32E Ch. 3.6 - Prob. 33E Ch. 3.6 - Prob. 34E Ch. 3.6 - Prob. 35E Ch. 3.6 - Prob. 36E Ch. 3.6 - Prob. 37E Ch. 3.6 - Prob. 38E Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Prob. 44E Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - Prob. 48E Ch. 3.6 - Use logarithmic differentiation to find the...Ch. 3.6 - Prob. 50E Ch. 3.6 - Prob. 51E Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Prob. 54E Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - A particle moves according to a law of motion s =...Ch. 3.7 - Prob. 4E Ch. 3.7 - Prob. 5E Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Prob. 9E Ch. 3.7 - Prob. 10E Ch. 3.7 - Prob. 11E Ch. 3.7 - Prob. 12E Ch. 3.7 - Prob. 13E Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - (a) The volume of a growing spherical cell is...Ch. 3.7 - Prob. 17E Ch. 3.7 - Prob. 18E Ch. 3.7 - The quantity of charge Q in coulombs (C) that has...Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E Ch. 3.7 - Prob. 22E Ch. 3.7 - Boyles Law states that when a sample of gas is...Ch. 3.7 - Prob. 24E Ch. 3.7 - Prob. 25E Ch. 3.7 - Prob. 26E Ch. 3.7 - The table shows how the average age of first...Ch. 3.7 - Refer to the law of laminar flow given in Example...Ch. 3.7 - Prob. 30E Ch. 3.7 - Prob. 31E Ch. 3.7 - The cost function for a certain commodity is C(q)...Ch. 3.7 - Prob. 33E Ch. 3.7 - Prob. 34E Ch. 3.7 - Patients undergo dialysis treatment to remove urea...Ch. 3.7 - Invasive species often display a wave of advance...Ch. 3.7 - Prob. 37E Ch. 3.7 - Prob. 38E Ch. 3.7 - Prob. 39E Ch. 3.8 - A population of protozoa develops with a constant...Ch. 3.8 - A common inhabitant of human intestines is the...Ch. 3.8 - A bacteria culture initially contains 100 cells...Ch. 3.8 - A bacteria culture grows with constant relative...Ch. 3.8 - The table gives estimates of the world population,...Ch. 3.8 - Prob. 6E Ch. 3.8 - Prob. 7E Ch. 3.8 - Strontium-90 has a half-life of 28 days. (a) A...Ch. 3.8 - Prob. 9E Ch. 3.8 - Prob. 10E Ch. 3.8 - Prob. 11E Ch. 3.8 - Dinosaur fossils are too old to be reliably dated...Ch. 3.8 - Dinosaur fossils are often dated by using an...Ch. 3.8 - Prob. 14E Ch. 3.8 - A roast turkey is taken from an oven when its...Ch. 3.8 - In a murder investigation, the temperature of the...Ch. 3.8 - Prob. 17E Ch. 3.8 - Prob. 18E Ch. 3.8 - Prob. 19E Ch. 3.8 - (a) If 1000 is borrowed at 8% interest, find the...Ch. 3.8 - Prob. 21E Ch. 3.8 - (a) How long will it take an investment to double...Ch. 3.9 - Prob. 1E Ch. 3.9 - (a) If A is the area of a circle with radius r and...Ch. 3.9 - Prob. 3E Ch. 3.9 - The length of a rectangle is increasing at a rate...Ch. 3.9 - A cylindrical tank with radius 5 m is being filled...Ch. 3.9 - Prob. 6E Ch. 3.9 - The radius of a spherical ball is increasing at a...Ch. 3.9 - Prob. 8E Ch. 3.9 - Suppose y=2x+1, where x and y are functions of t....Ch. 3.9 - Prob. 10E Ch. 3.9 - If x2 + y2 + z2 = 9, dx/dt = 5, and dy/dt = 4,...Ch. 3.9 - A particle is moving along a hyperbola xy = 8. As...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - (a) What quantities are given in the problem? (b)...Ch. 3.9 - Two cars start moving from the same point. One...Ch. 3.9 - Prob. 18E Ch. 3.9 - A man starts walking north at 4 ft/s from a point...Ch. 3.9 - A baseball diamond is a square with side 90 ft. A...Ch. 3.9 - Prob. 21E Ch. 3.9 - A boat is pulled into a dock by a rope attached to...Ch. 3.9 - Prob. 23E Ch. 3.9 - Prob. 24E Ch. 3.9 - Water is leaking out of an inverted conical tank...Ch. 3.9 - A trough is 10 ft long and its ends have the shape...Ch. 3.9 - A water trough is 10m long and a cross-section has...Ch. 3.9 - Prob. 28E Ch. 3.9 - Gravel is being dumped from a conveyor belt at a...Ch. 3.9 - A kite 100ft above the ground moves horizontally...Ch. 3.9 - The sides of an equilateral triangle are...Ch. 3.9 - How fast is the angle between the ladder and the...Ch. 3.9 - Prob. 33E Ch. 3.9 - Prob. 34E Ch. 3.9 - If the minute hand of a clock has length r (in...Ch. 3.9 - Prob. 36E Ch. 3.9 - Boyles Law states that when a sample of gas is...Ch. 3.9 - When air expands adiabatically (without gaining or...Ch. 3.9 - Prob. 39E Ch. 3.9 - Prob. 40E Ch. 3.9 - Prob. 41E Ch. 3.9 - Two carts, A and B, are connected by a rope 39 ft...Ch. 3.9 - Prob. 43E Ch. 3.9 - A lighthouse is located on a small island 3 km...Ch. 3.9 - Prob. 45E Ch. 3.9 - Prob. 46E Ch. 3.9 - Prob. 47E Ch. 3.9 - Prob. 48E Ch. 3.9 - Prob. 49E Ch. 3.9 - Prob. 50E Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linearization L(x) of the function at n....Ch. 3.10 - Find the linear approximation of the function...Ch. 3.10 - Prob. 6E Ch. 3.10 - Prob. 7E Ch. 3.10 - Prob. 8E Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Verify the given linear approximation at a = 0....Ch. 3.10 - Find the differential of each function. 11. (a) y...Ch. 3.10 - Prob. 12E Ch. 3.10 - Find the differential of each function. 13. (a)...Ch. 3.10 - Prob. 14E Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - Prob. 16E Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - (a) Find the differential dy and (b) evaluate dy...Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Prob. 20E Ch. 3.10 - Prob. 21E Ch. 3.10 - Compute y and dy for the given values of x and dx...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Prob. 24E Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Use a linear approximation (or differentials) to...Ch. 3.10 - Prob. 27E Ch. 3.10 - Prob. 28E Ch. 3.10 - Prob. 29E Ch. 3.10 - Explain, in terms of linear approximations or...Ch. 3.10 - Prob. 31E Ch. 3.10 - Prob. 32E Ch. 3.10 - Prob. 33E Ch. 3.10 - Prob. 34E Ch. 3.10 - The circumference of a sphere was measured to be...Ch. 3.10 - Use differentials to estimate the amount of paint...Ch. 3.10 - Prob. 37E Ch. 3.10 - Prob. 38E Ch. 3.10 - Prob. 39E Ch. 3.10 - When blood flows along a blood vessel, the flux F...Ch. 3.10 - Prob. 41E Ch. 3.10 - On page 431 of Physics: Calculus, 2d ed., by...Ch. 3.10 - Prob. 43E Ch. 3.10 - Prob. 44E Ch. 3.11 - Find the numerical value of each expression. 1....Ch. 3.11 - Find the numerical value of each expression. 2....Ch. 3.11 - Prob. 3E Ch. 3.11 - Prob. 4E Ch. 3.11 - Prob. 5E Ch. 3.11 - Prob. 6E Ch. 3.11 - Prob. 7E Ch. 3.11 - Prob. 8E Ch. 3.11 - Prob. 9E Ch. 3.11 - Prob. 10E Ch. 3.11 - Prob. 11E Ch. 3.11 - Prob. 12E Ch. 3.11 - Prob. 13E Ch. 3.11 - Prob. 14E Ch. 3.11 - Prove the identity. 15. sinh 2x = 2 sinh x cosh x Ch. 3.11 - Prob. 16E Ch. 3.11 - Prob. 17E Ch. 3.11 - Prob. 18E Ch. 3.11 - Prove the identity. 19. (cosh x + sinh x)n = cosh...Ch. 3.11 - Prob. 20E Ch. 3.11 - Prob. 21E Ch. 3.11 - Prob. 22E Ch. 3.11 - Prob. 23E Ch. 3.11 - Prob. 24E Ch. 3.11 - Prob. 25E Ch. 3.11 - Prob. 26E Ch. 3.11 - Prob. 27E Ch. 3.11 - Prob. 28E Ch. 3.11 - Prob. 29E Ch. 3.11 - Prob. 30E Ch. 3.11 - Prob. 31E Ch. 3.11 - Prob. 32E Ch. 3.11 - Prob. 33E Ch. 3.11 - Prob. 34E Ch. 3.11 - Prob. 35E Ch. 3.11 - Find the derivative. Simplify where possible. 36....Ch. 3.11 - Find the derivative. Simplify where possible. 37....Ch. 3.11 - Prob. 38E Ch. 3.11 - Prob. 39E Ch. 3.11 - Find the derivative. Simplify where possible. 40....Ch. 3.11 - Find the derivative. Simplify where possible. 41....Ch. 3.11 - Prob. 42E Ch. 3.11 - Prob. 43E Ch. 3.11 - Prob. 44E Ch. 3.11 - Prob. 45E Ch. 3.11 - Prob. 46E Ch. 3.11 - Prob. 47E Ch. 3.11 - Prob. 48E Ch. 3.11 - Prob. 49E Ch. 3.11 - Prob. 50E Ch. 3.11 - Prob. 51E Ch. 3.11 - Prob. 52E Ch. 3.11 - A cable with linear density = 2 kg/m is strung...Ch. 3.11 - A model for the velocity of a falling object after...Ch. 3.11 - Prob. 55E Ch. 3.11 - Prob. 56E Ch. 3.11 - Prob. 57E Ch. 3.11 - Prob. 58E Ch. 3 - State each differentiation rule both in symbols...Ch. 3 - Prob. 2RCC Ch. 3 - Prob. 3RCC Ch. 3 - Prob. 4RCC Ch. 3 - Give several examples of how the derivative can be...Ch. 3 - Prob. 6RCC Ch. 3 - Prob. 7RCC Ch. 3 - Prob. 1RQ Ch. 3 - Prob. 2RQ Ch. 3 - Prob. 3RQ Ch. 3 - Prob. 4RQ Ch. 3 - Prob. 5RQ Ch. 3 - Prob. 6RQ Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Prob. 8RQ Ch. 3 - Prob. 9RQ Ch. 3 - Prob. 10RQ Ch. 3 - Prob. 11RQ Ch. 3 - Prob. 12RQ Ch. 3 - Prob. 13RQ Ch. 3 - Prob. 14RQ Ch. 3 - Determine whether the statement is true or false....Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Calculate y'. 12. y = (arcsin 2x)2 Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Calculate y'. 17. y=arctan Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Calculate y'. 30. y=(x2+1)4(2x+1)3(3x1)5 Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Prob. 82RE Ch. 3 - Prob. 83RE Ch. 3 - Prob. 84RE Ch. 3 - Prob. 85RE Ch. 3 - Prob. 86RE Ch. 3 - Prob. 87RE Ch. 3 - A particle moves along a horizontal line so that...Ch. 3 - A particle moves on a vertical line so that its...Ch. 3 - Prob. 90RE Ch. 3 - Prob. 91RE Ch. 3 - Prob. 92RE Ch. 3 - Prob. 93RE Ch. 3 - Prob. 94RE Ch. 3 - Prob. 95RE Ch. 3 - Prob. 96RE Ch. 3 - Prob. 97RE Ch. 3 - Prob. 98RE Ch. 3 - A balloon is rising at a constant speed of 5 ft/s....Ch. 3 - Prob. 100RE Ch. 3 - Prob. 101RE Ch. 3 - Prob. 102RE Ch. 3 - Prob. 103RE Ch. 3 - Prob. 104RE Ch. 3 - Prob. 105RE Ch. 3 - Prob. 106RE Ch. 3 - Prob. 107RE Ch. 3 - Prob. 108RE Ch. 3 - Prob. 109RE Ch. 3 - Suppose f is a differentiable function such that...Ch. 3 - Prob. 111RE Ch. 3 - Prob. 112RE Ch. 3 - Prob. 1P Ch. 3 - Prob. 2P Ch. 3 - Prob. 3P Ch. 3 - Prob. 4P Ch. 3 - Prob. 5P Ch. 3 - Prob. 6P Ch. 3 - Prob. 7P Ch. 3 - Prob. 8P Ch. 3 - Prob. 9P Ch. 3 - Prob. 10P Ch. 3 - Prob. 11P Ch. 3 - Prob. 12P Ch. 3 - Prob. 13P Ch. 3 - If f(x)=x46+x45+21+x, calculate f(46)(3). Express...Ch. 3 - The figure shows a rotating wheel with radius 40...Ch. 3 - Prob. 16P Ch. 3 - Prob. 17P Ch. 3 - Prob. 18P Ch. 3 - Let T and N be the tangent and normal lines to the...Ch. 3 - Prob. 20P Ch. 3 - Prob. 21P Ch. 3 - Let P(x1, y1) be a point on the parabola y2 = 4px...Ch. 3 - Prob. 23P Ch. 3 - Prob. 24P Ch. 3 - Prob. 25P Ch. 3 - Prob. 27P Ch. 3 - Prob. 28P Ch. 3 - Prob. 29P Ch. 3 - Prob. 30P Ch. 3 - Find the two points on the curve y = x4 2x2 x...Ch. 3 - Prob. 32P Ch. 3 - Prob. 33P Ch. 3 - Prob. 34P Ch. 3 - Prob. 35P

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