Problem 1E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=(x+1)99 Problem 2E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w=(t3+1)100 Problem 3E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. g(x)=(4x2+1)7 Problem 4E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=1x2 Problem 5E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=ex+1 Problem 6E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w=(t+1)100 Problem 7E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. h(w)=(w42w)5 Problem 8E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. s(t)=(3t2+4t+1)3 Problem 9E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w(r)=r4+1 Problem 10E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. k(x)=(x3+ex)4 Problem 11E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=e2x(x2+5x) Problem 12E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=e3w/2 Problem 13E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. g(x)=ex Problem 14E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. B=15e0.20t Problem 15E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w=100ex2 Problem 16E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f()=2 Problem 17E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=(x+2) Problem 18E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. g(x)=3(2x+7) Problem 19E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(t)=te52t Problem 20E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. p(t)=e4t+2 Problem 21E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. v(t)=t2ect Problem 22E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. g(t)=e(1+3t)2 Problem 23E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w=es Problem 24E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=e4t Problem 25E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=s3+1 Problem 26E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=tet2 Problem 27E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(z)=zez Problem 28E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. z(x)=2x+53 Problem 29E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. z=25t3 Problem 30E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w=(x25x)3 Problem 31E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(y)=10(5y) Problem 32E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(z)=zez Problem 33E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=z2z Problem 34E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=(x2+23)2 Problem 35E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. h(x)=x2+9x+3 Problem 36E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=exexex+ex Problem 37E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=1e3x+x2 Problem 38E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. h(z)=(ba+z2)4 Problem 39E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=1x3+1 Problem 40E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(z)=1(ez+1)2 Problem 41E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. w=(t2+3t)(1e2t) Problem 42E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. h(x)=2e3x Problem 43E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=6e5x+ex2 Problem 44E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=e(x1)2 Problem 45E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(w)=(5w2+3)ew2 Problem 46E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f()=(e+e)1 Problem 47E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=e3t2+5 Problem 48E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. z=(te3t+e5t)9 Problem 49E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(y)=ee(y2) Problem 50E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(t)=2e2e2t Problem 51E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=(ax2+b)3 Problem 52E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(t)=aebt Problem 53E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. f(x)=axebx Problem 54E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. g()=ee2 Problem 55E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=aebecx Problem 56E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=(exex)2 Problem 57E: In Exercises 157, find the derivatives. Assume that a, b, and c are constants. y=(x2+5)3(3x32)2 Problem 58E: In Problems 5861, use Figure 3.16 and the chain rule to estimate the derivative, or state why the... Problem 59E: In Problems 5861, use Figure 3.16 and the chain rule to estimate the derivative, or state why the... Problem 60E: In Problems 5861, use Figure 3.16 and the chain rule to estimate the derivative, or state why the... Problem 61E: In Problems 5861, use Figure 3.16 and the chain rule to estimate the derivative, or state why the... Problem 62E: In Problems 6265, use Figure 3.17 to evaluate the derivative. Figure 3.17 ddxf(g(x))x=30 Problem 63E: In Problems 6265, use Figure 3.17 to evaluate the derivative. Figure 3.17 ddxf(g(x))x=70 Problem 64E: In Problems 6265, use Figure 3.17 to evaluate the derivative. Figure 3.17 ddxg(f(x))x=30 Problem 65E: In Problems 6265, use Figure 3.17 to evaluate the derivative. Figure 3.17 ddxg(f(x))x=70 Problem 66E: Find the equation of the tangent line to f(x) = (x 1)3 at the point where x = 2. Problem 67E: Find the equation of the line tangent to y = f(x) at x = 1, where f(x)=6e5x+ex2. Problem 68E: Find the equation of the line tangent to f(t) = 100e0.3t at t = 2. Problem 69E: For what values of x is the graph of y=ex2 concave down? Problem 70E: For what intervals is f(x)=xex concave down? Problem 71E: Suppose f(x)=(2x+1)10(3x1)7. Find a formula for f (x). Decide on a reasonable way to simplify your... Problem 72E: Find a possible formula for a function m(x) such that m(x)=x5e(x6). Problem 73E: Given F(2) = 1, F(2) = 5, F(4) = 3, F(4) = 7 and G(4) = 2, G(4) = 6, G(3) = 4, G(3) = 8, find: (a)... Problem 74E: Given f(x) with f(1) = 2 and f (1) = 5, find (a) g(1) if g(x)=(f(x))3 (b) h(1) if h(x)=f(x3) Problem 75E: Given f(x) with f(2) = 7 and f (2) = 3 and f (4) = 2 find (a) g(2) if g(x)=(f(x))2 (b) h(2) if... Problem 76E: A particle is moving on the x-axis, where x is in centimeters. Its velocity, , in cm/sec, when it is... Problem 77E: A fish population is approximated by P(t)=10e0.6t, where t is in months. Calculate and use units to... Problem 78E: The worlds population8 is about f(t)=7.17e0.011t billion, where t is time in years since July 2014.... Problem 79E: Fourth-quarter net sales for the Hershey Company9, in billion dollars, in t years from 2012 can be... Problem 80E: For t in years since 2010, daily oil consumption in China, in thousands of barrels, was approximated... Problem 81E: The balance in a bank account t years after money is deposited is given by f(t)=5000e0.02t dollars.... Problem 82E: For t 0 in minutes, the temperature, H, of a pot of soup in degrees Celsius is11 H=5+95e0.054t. (a)... Problem 83E: A yam is put in a hot oven, maintained at a constant temperature 200C. At time t = 30 minutes, the... Problem 84E: The 2010 census12 determined the population of the US was 308.75 million on April 1, 2010. If the... Problem 85E: If you invest P dollars in a bank account at an annual interest rate of r%, then after t years you... Problem 86E: The theory of relativity predicts that an object whose mass is m0 when it is at rest will appear... Problem 87E: Since the 1950s, the carbon dioxide concentration in the air has been recorded at the Mauna Loa... Problem 88E: Instruments on a plane measure the distance traveled, x (in km), and the quantity of fuel in the... Problem 89E: For Problems 8992, if f(x) has a positive slope everywhere, and g(x) has a negative slope... Problem 90E: For Problems 8992, if f(x) has a positive slope everywhere, and g(x) has a negative slope... Problem 91E: For Problems 8992, if f(x) has a positive slope everywhere, and g(x) has a negative slope... Problem 92E: For Problems 8992, if f(x) has a positive slope everywhere, and g(x) has a negative slope... Problem 93E: In Problems 9395, explain what is wrong with the statement. The derivative of g(x)=(ex+2)5 is... Problem 94E: In Problems 9395, explain what is wrong with the statement. The derivative of w(x)=ex2 is w(x)=ex2. Problem 95E: In Problems 9395, explain what is wrong with the statement. If f(x)=h(g(x)) and h(3) = 0, then f (3)... Problem 96E: In Problems 9697, give an example of: A function involving a sine and an exponential that requires... Problem 97E: In Problems 9697, give an example of: A function that can be differentiated both using the chain... Problem 98E: Are the statements in Problems 98101 true or false? If a statement is true, explain how you know. If... Problem 99E: Are the statements in Problems 98101 true or false? If a statement is true, explain how you know. If... Problem 100E: Are the statements in Problems 98101 true or false? If a statement is true, explain how you know. If... Problem 101E: Are the statements in Problems 98101 true or false? If a statement is true, explain how you know. If... format_list_bulleted