Problem 1E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 2E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 3E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 4E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 5E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 6E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 7E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 8E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 9E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 10E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 11E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 12E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 13E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 14E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 15E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 16E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 17E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 18E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 19E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 20E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 21E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 22E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 23E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 24E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 25E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 26E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 27E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 28E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 29E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 30E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 31E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 32E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 33E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 34E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 35E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 36E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 37E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 38E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 39E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 40E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 41E: For Exercises 141, find the derivative. It may be to your advantage to simplify before... Problem 42E: Let f(x) = ln(3x). (a) Find f(x) and simplify your answer. (b) Use properties of logs to rewrite... Problem 43E: On what intervals is ln(x2 + 1) concave up? Problem 44E: Use the chain rule to obtain the formula for ddx(arcsinx) Problem 45E: Using the chain rule, find ddx(logx). (Recall log x = log10 x.) Problem 46E: To compare the acidity of different solutions, chemists use the pH (which is a single number, not... Problem 47E: The number of years, T, it takes an investment of 1000 to grow to F in an account which pays 5%... Problem 48E: A firm estimates that the total revenue, R, in dollars, received from the sale of q goods is given... Problem 49E: Average leaf width, w (in mm), in tropical Australia17 is a function of the average annual rainfall,... Problem 50E: (a) Find the equation of the tangent line to y = ln x at x = 1. (b) Use it to calculate approximate... Problem 51E: (a) For x 0, find and simplify the derivative of f(x) = arctan x + arctan(1x). (b) What does your... Problem 52E: (a) Given that f(x) = x3, find f(2). (b) Find f1(x). (c) Use your answer from part (b) to find... Problem 53E: (a) For f(x) = 2x5 + 3x3 + x, find f(x). (b) How can you use your answer to part (a) to determine if... Problem 54E: Imagine you are zooming in on the graph of each of the following functions near the origin: y = x y... Problem 55E: In Problems 5558, use Figure 3.25 to find a point x where (x) = n(m(x)) has the given derivative.... Problem 56E: In Problems 5558, use Figure 3.25 to find a point x where (x) = n(m(x)) has the given derivative.... Problem 57E: In Problems 5558, use Figure 3.25 to find a point x where (x) = n(m(x)) has the given derivative.... Problem 58E: In Problems 5558, use Figure 3.25 to find a point x where (x) = n(m(x)) has the given derivative.... Problem 59E: In Problems 5961, use Figure 3.26 to estimate the derivatives. Figure 3.26 (f1)(5) Problem 60E: In Problems 5961, use Figure 3.26 to estimate the derivatives. Figure 3.26 (f1)(10) Problem 61E: In Problems 5961, use Figure 3.26 to estimate the derivatives. Figure 3.26 (f1)(15) Problem 62E: In Problems 6264, use Figure 3.27 to calculate the derivative. Figure 3.27 (2) if (x) = (f(x))3 Problem 63E: In Problems 6264, use Figure 3.27 to calculate the derivative. Figure 3.27 k(2) if k(x) = (f(x))1 Problem 64E: In Problems 6264, use Figure 3.27 to calculate the derivative. Figure 3.27 g(5) if g(x) = f1(x) Problem 65E: Use the table and the fact that f(x) is invertible and differentiable everywhere to find (f1)(3). Problem 66E: At a particular location, f(p) is the number of gallons of gas sold when the price is p dollars per... Problem 67E: Let P = f(t) give the US population18 in millions in year t. (a) What does the statement f(2014) =... Problem 68E: Figure 3.28 shows the number of motor vehicles,19 f(t), in millions, registered in the world t years... Problem 69E: Using Figure 3.29, where f(2) = 2.1, f(4) = 3.0, f(6) = 3.7, f(8) = 4.2, find (f1)(8). Figure 3.29 Problem 70E: Figure 3.30 shows an invertible function f(x). (a) Sketch a graph of f1(x). (b) Find each x-value... Problem 71E: An invertible function f(x) has values in the table. Evaluate (a) f(a)(f1)(A) (b) f(b)(f1)(B) (c) f... Problem 72E: Assuming g(x) 0, use the chain rule to explain why the derivative of f(x) = ln(g(x)) is zero... Problem 73E: If f is continuous, invertible, and defined for all x, why must at least one of the statements... Problem 74E: Suppose f(x) is an invertible function that is differentiable at every point of its domain and let... Problem 75E: In Problems 7577, explain what is wrong with the statement. If w(x) = ln(1 + x4) then w(x) = 1(1 +... Problem 76E: In Problems 7577, explain what is wrong with the statement. The derivative of f(x) = ln(ln x) is... Problem 77E: In Problems 7577, explain what is wrong with the statement. Given f(2) = 6, f(2) = 3, and f1(3) = 4,... Problem 78E: In Problems 7881, give an example of: A function that is equal to a constant multiple of its... Problem 79E: In Problems 7881, give an example of: A function whose derivative is cx, where c is a constant. Problem 80E: In Problems 7881, give an example of: A function f(x) for which f(x) = f(cx), where c is a constant. Problem 81E: In Problems 7881, give an example of: A function f such that ddx(f1(x))=1f(x)=1. Problem 82E: Are the statements in Problems 8283 true or false? Give an explanation for your answer. The graph of... Problem 83E: Are the statements in Problems 8283 true or false? Give an explanation for your answer. If f(x) has... format_list_bulleted