Problem 1E: Chain Rule Describe the Chain Rule for the composition of two differentiate functions in your own... Problem 2E: General Power Rule What is the difference between the (Simple) Power Rule and the General Power... Problem 3E Problem 4E: Derivatives for Bases Other than e What are the values of a and b? ddx[64x]=a(lnb)64x Problem 5E Problem 6E Problem 7E: Decomposition of a Composite Function In Exercises 5-12, complete the table. y=f(g(x)) u=g(x) y=f(u)... Problem 8E: Decomposition of a Composite Function In Exercises 5-12, complete the table. y=f(g(x)) u=g(x) y=f(u)... Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E: Finding a Derivative In Exercises 13-32, find the derivative of the function. y=5(2x3)4 Problem 15E: Finding a Derivative In Exercises 13-32, find the derivative of the function. g(x)=3(49x)5/6 Problem 16E: Finding a Derivative In Exercises 13-32, find the derivative of the function. f(t)=(9t+2)2/3 Problem 17E: Finding a Derivative In Exercises 13-32, find the derivative of the function. h(s)=25s2+3 Problem 18E: Finding a Derivative In Exercises 13-32, find the derivative of the function. y=6x2+13 Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E: Finding a Derivative In Exercises 13-32, find the derivative of the function. y=13x+5 Problem 24E Problem 25E: Finding a Derivative In Exercises 13-32, find the derivative of the function. f(x)=x(2x5)3 Problem 26E: Finding a Derivative In Exercises 13-32, find the derivative of the function. y=x216x2 Problem 27E Problem 28E: Finding a Derivative In Exercises 13-32, find the derivative of the function. y=xx2+4 Problem 29E Problem 30E: Finding a Derivative In Exercises 13-32, find the derivative of the function. g(x)=(3x222x+3)2 Problem 31E: Finding a Derivative In Exercises 13-32, find the derivative of the function. f(x)=[(x2+3)5+x]2 Problem 32E: Finding a Derivative In Exercises 13-32, find the derivative of the function. g(x)=[2+(x2+1)4]3 Problem 33E Problem 34E: Finding a Derivative of a Trigonometric Function In Exercises 33-50, find the derivative of the... Problem 35E Problem 36E: Finding a Derivative of a Trigonometric Function In Exercises 33-50, find the derivative of the... Problem 37E: Finding a Derivative of a Trigonometric Function In Exercises 33-50, find the derivative of the... Problem 38E Problem 39E Problem 40E: Finding a Derivative of a Trigonometric Function In Exercises 33-50, find the derivative of the... Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E: Finding a Derivative of a Trigonometric Function In Exercises 33-50, find the derivative of the... Problem 49E Problem 50E: Finding a Derivative of a Trigonometric Function In Exercises 33-50, find the derivative of the... Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E: Finding a Derivative of an Exponential Function In Exercises 57-72, find the derivative of the... Problem 59E Problem 60E Problem 61E Problem 62E: Finding a Derivative of an Exponential Function In Exercises 57-72, find the derivative of the... Problem 63E Problem 64E: Finding a Derivative of an Exponential Function In Exercises 57-72, find the derivative of the... Problem 65E Problem 66E Problem 67E Problem 68E: Finding a Derivative of an Exponential Function In Exercises 57-72, find the derivative of the... Problem 69E Problem 70E: Finding a Derivative of an Exponential Function In Exercises 57-72, find the derivative of the... Problem 71E Problem 72E: Finding a Derivative of an Exponential Function In Exercises 57-72, find the derivative of the... Problem 73E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 74E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 75E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 83E Problem 84E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 85E Problem 86E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 87E Problem 88E: Finding a Derivative of a Logarithmic Function In Exercises 73-94, find the derivative of the... Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E: Slope of a Tangent Line In Exercises 95 and 96. find the slope of the tangent line to the sine... Problem 97E Problem 98E Problem 99E Problem 100E Problem 101E Problem 102E Problem 103E Problem 104E Problem 105E Problem 106E Problem 107E Problem 108E Problem 109E Problem 110E Problem 111E Problem 112E Problem 113E Problem 114E Problem 115E Problem 116E Problem 117E Problem 118E Problem 119E: Horizontal Tangent Line Determine the point(s) in the interval (0,2) at which the graph of... Problem 120E: Horizontal Tangent Line Determine the point(s) at which the graph of f(x)=4x2x1 has a horizontal... Problem 121E Problem 122E Problem 123E: Finding a Second Derivative In Exercises 121-128, find the second derivative of the function.... Problem 124E Problem 125E Problem 126E Problem 127E Problem 128E: Finding a Second Derivative In Exercises 121-128, find the second derivative of the function.... Problem 129E Problem 130E Problem 131E Problem 132E: Evaluating a Second Derivative In Exercises 129-132, evaluate the second derivative of the function... Problem 133E Problem 134E: Finding a Derivative In Exercises 133-148, find the derivative of the function. g(x)=5x Problem 135E Problem 136E Problem 137E Problem 138E Problem 139E Problem 140E Problem 141E Problem 142E: Finding a Derivative In Exercises 133-148, find the derivative of the function. y=log102x Problem 143E Problem 144E Problem 145E Problem 146E: Finding a Derivative In Exercises 133-148, find the derivative of the function. h(x)=log3xx12 Problem 147E Problem 148E Problem 149E Problem 150E: Identifying Graphs In Exercises 149 and 150, the graphs of a function f and its derivative f' are... Problem 151E Problem 152E Problem 153E Problem 154E Problem 155E Problem 156E Problem 157E: Pendulum A 15-centimeter pendulum moves according to the equation =0.2cos8t where is the angular... Problem 158E: Harmonic Motion The displacement from equilibrium of an object in harmonic motion on the end of a... Problem 159E Problem 160E Problem 161E Problem 162E: Wave Motion A buoy oscillates in simple harmonic motion y=Acost as waves move past it. The buoy... Problem 163E: Modeling Data The table shows the temperatures T (in degrees Fahrenheit) at which water boils at... Problem 164E Problem 165E Problem 166E Problem 167E Problem 168E: Conjecture Let f be a differentiable function of period p. (a) Is the function f' periodic? Verify... Problem 169E: Think About It Let r(x)=f(g(x)) and s(x)=g(f(x)), where f and g are shown in the figure. Find (a)... Problem 170E: Using Trigonometric Functions (a) Find the derivative of the function g(x)=sin2x+cos2x in two ways.... Problem 171E Problem 172E Problem 173E Problem 174E Problem 175E Problem 176E Problem 177E Problem 178E Problem 179E Problem 180E: Linear and Quadratic Approximations The linear and quadratic approximations or a function f at x=a... Problem 181E: True or False? In Exercises 181-184, determine whether the statement is true or false, if it is... Problem 182E Problem 183E: True or False? In Exercises 181-184, determine whether the statement is true or false. If it is... Problem 184E Problem 185E: Let f(x)=a1sinx+a2sin2x++annx where a1,a2,,an are real numbers and where n is a positive integer.... Problem 186E format_list_bulleted