1 Functions And Models 2 Limits And Derivatives 3 Differentiation Rules 4 Applications Of Differentiation 5 Integrals 6 Applications Of Integration 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Sequences, Series, And Power Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G The Logarithm Defined As An Integral expand_more
3.1 Derivatives Of Polynomials And Exponential Functions 3.2 The Product And Quotient Rules 3.3 Derivatives Of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives Of Logarithmic And Inverse Trigonometric Functions 3.7 Rates Of Change In The Natural And Social Sciences 3.8 Exponential Growth And Decay 3.9 Related Rates 3.10 Linear Approximations And Differentials 3.11 Hyperbolic Functions Chapter Questions expand_more
Problem 1E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer... Problem 2E Problem 3E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer... Problem 4E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer... Problem 5E: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the... Problem 6E: Write the composite function in the form f(g(x)) . [Identify the inner function u=g(x) and the outer... Problem 7E: Find the derivative of the function. 7. f(x)=2x35x2+45 Problem 8E: Find the derivative of the function. 8. f(x)=x5+3x2x50 Problem 9E: Find the derivative of the function. f(x)=5x+1 Problem 10E: Find the derivative of the function. f(x)=1x213 Problem 11E: Find the derivative of the function. 11. g(t)=1(2t+1)2 Problem 12E Problem 13E: Find the derivative of the function. f() = cos(2) Problem 14E: Find the derivative of the function. g() = cos2 Problem 15E: Find the derivative of the function. 15. g(x)=ex2x Problem 16E: Find the derivative of the function. 16. y=5x Problem 17E: Find the derivative of the function. y = x2e3x Problem 18E: Find the derivative of the function. f(t) = t sin t Problem 19E: Find the derivative of the function. f(t) = eat sin bt Problem 20E Problem 21E: Find the derivative of the function. 21. F(x)=(4x+5)3x22x+54 Problem 22E: Find the derivative of the function. 22. G(z)=(14z)2z2+1 Problem 23E: Find the derivative of the function. y=xx+1 Problem 24E: Find the derivative of the function. y=(x+1x)5 Problem 25E: Find the derivative of the function. y = e tan Problem 26E: Find the derivative of the function. f(t)2t3 Problem 27E: Find the derivative of the function. g(u)=(u31u3+1)8 Problem 28E: Find the derivative of the function. s(t)=1+sint1+cost Problem 29E: Find the derivative of the function. r(t)=10t2 Problem 30E: Find the derivative of the function. f(z) = ez/(z1) Problem 31E: Find the derivative of the function. H(r)=(r21)3(2r+1)5 Problem 32E: Find the derivative of the function. J() = tan2(n) Problem 33E: Find the derivative of the function. F(t) = et sin 2t Problem 34E: Find the derivative of the function. F(t)=t2t3+1 Problem 35E: Find the derivative of the function. G(x) = 4C/x Problem 36E Problem 37E Problem 38E Problem 39E: Find the derivative of the function. 39. F(t)=tan1+t2 Problem 40E Problem 41E: Find the derivative of the function. 41. y= sin 2 x 2 +1 Problem 42E: Find the derivative of the function. y = esin 2x + sin(e2x) Problem 43E: Find the derivative of the function. 43. g(x)=sinex1+ex Problem 44E: Find the derivative of the function. 44. f(t)=e1/tt21 Problem 45E: Find the derivative of the function. f(t) = tan(sec(cos t)) Problem 46E: Find the derivative of the function. y=x+x+x Problem 47E: Find the derivative of the function. 47. f(x)=esin2x2 Problem 48E: Find the derivative of the function. y=234x Problem 49E: Find the derivative of the function. 49. y=3cosx214 Problem 50E: Find the derivative of the function. 50. y=sin(+tan(+cos)) Problem 51E: Find the derivative of the function. y=cossin(tanx) Problem 52E: Find the derivative of the function. 52. y=sin3cosx2 Problem 53E: Find y and y. y = cos(sin 3) Problem 54E: Find y and y . 54. y=(1+x)3 Problem 55E Problem 56E: Find y and y. y=eex Problem 57E: Find an equation of the tangent line to the curve at the given point. y = 2x, (0. 1) Problem 58E: Find an equation of the tangent line to the curve at the given point. y=1+x3,(2,3) Problem 59E: Find an equation of the tangent line to the curve at the given point. y = sin(sin x), (, 0) Problem 60E: Find an equation of the tangent line to the curve at the given point. y=xex2,(0,0) Problem 61E Problem 62E: (a) The curve y=|x|/2x2 is called a bullet-nose curve. Find an equation of the tangent line to this... Problem 63E: (a) If f(x)=2x2x, find f(x). (b) Check to see that your answer to part (a) is reasonable by... Problem 64E Problem 65E: Find all points on the graph of the function f(x) = 2 sin x + sin2x at which the tangent line is... Problem 66E: At what point on the curve y=1+2x is the tangent line perpendicular to the line 6x + 2y = 1? Problem 67E: If F(x) = f(g(x)), where f(2) = 8, f(2) = 4, f(5) = 3, g(5) = 2, and g(5) = 6, find F(5). Problem 68E: If h(x)=4+3f(x), where f(1) = 7andf(1) = 4, find h(1). Problem 69E: A table of values for f, g, f, and g is given. (a) If h(x) = f(g(x)), find h(1). (b) If H(x) =... Problem 70E: Let f and g be the functions in Exercise 69. (a) If F(x)=f(f(x)) , find F(2) . (b) If G(x)=g(g(x)) ,... Problem 71E: If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) =... Problem 72E: If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x2). Use the graph of f... Problem 73E: If g(x)=f(x), where the graph off is shown, evaluate g(3). Problem 74E Problem 75E: Suppose f is differentiable on . Let F(x) = f(ex) and G(x) = ef(x). Find expressions for (a) F(x)... Problem 76E: Let g(x) = ecx + f(x) and h(x) = ekxf(x), where f(0) = 3, f(0) = 5, and f(0) = 2. (a) Find g(0) and... Problem 77E: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h(1) = 4, g(2) = 5, and f(3) = 6. Find r(1). Problem 78E: If g is a twice differentiable function and f(x) = xg(x2), find f in terms of g, g, and g. Problem 79E Problem 80E Problem 81E: Show that the function y = e2x (A cos 3x + B sin 3x) satisfies the differential equation y 4y + 13y... Problem 82E: For what values of r does the function y = erx satisfy the differential equation y 4y + y = 0? Problem 83E: Find the 50th derivative of y = cos 2x. Problem 84E Problem 85E: The displacement of a particle on a vibrating string is given by the equation s(t)=10+14sin(10t)... Problem 86E: If the equation of motion of a particle is given by s = A cos(t + ), the particle is said to undergo... Problem 87E: A Cepheid variable star is a star whose brightness alternately increases and decreases. The most... Problem 88E: In Example 1.3.4 we arrived at a model for the length of daylight (in hours) in Philadelphia on the... Problem 89E Problem 90E: Under certain circumstance a rumor spreads according to the equation p(t)=11+aekt where p(t) is the... Problem 91E: The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption... Problem 92E: Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is... Problem 93E Problem 94E Problem 95E: Use the Chain Rule to prove the following. (a) The derivative of an even function is an odd... Problem 96E Problem 97E: Use the Chain Rule to show that if is measured in degrees, then dd(sin)=180cos (This gives one... Problem 98E Problem 99E Problem 100E Problem 101E Problem 102E Problem 1AP: An approach path for an aircraft landing is shown in the figure and satisfies the following... Problem 2AP Problem 3AP Problem 4AP format_list_bulleted
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