 4.5.1E: Find the derivative of the function.y = ln(8x)
 4.5.2E: Find the derivative of the function.y = ln(?4x)
 4.5.3E: Find the derivative of the function.y = ln(8?3x)
 4.5.4E: Find the derivative of the function.y =ln(1 + x3)
 4.5.5E: Find the derivative of the function.y = ln4x2 ? 9x
 4.5.6E: Find the derivative of the function.y = ln ?8x3 + 2x
 4.5.7E: Find the derivative of the function.
 4.5.8E: Find the derivative of the function.
 4.5.9E: Find the derivative of the function.y = ln(x4 + 5x2)3/2
 4.5.10E: Find the derivative of the function.y = ln(5x3 ? 2x)3/2
 4.5.11E: Find the derivative of the function.y = ?5x ln(3x + 2)
 4.5.12E: Find the derivative of the function.y = (3x + 7) ln(2x ? 1)
 4.5.13E: Find the derivative of the function.s = t2 lnt
 4.5.14E: Find the derivative of the function.y = x ln2 ? x2
 4.5.15E: Find the derivative of the function.
 4.5.16E: Find the derivative of the function.
 4.5.17E: Find the derivative of the function.
 4.5.18E: Find the derivative of the function.
 4.5.19E: Find the derivative of the function.
 4.5.20E: Find the derivative of the function.
 4.5.21E: Find the derivative of the function.y = (lnx + 1)4
 4.5.22E: Find the derivative of the function.
 4.5.23E: Find the derivative of the function.y = ln ln x
 4.5.24E: Find the derivative of the function.y = (ln 4)(ln 3x)
 4.5.25E: Find the derivative of the function.
 4.5.26E: Find the derivative of the function.y = e2x1 ln(2x ? 1)
 4.5.27E: Find the derivative of the function.
 4.5.28E: Find the derivative of the function.
 4.5.29E: Find the derivative of the function.g(z) = (e2z + ln z)3
 4.5.30E: Find the derivative of function.
 4.5.31E: Find the derivative of the function.y = log(6x)
 4.5.32E: Find the derivative of the function.y = log(4x ? 3)
 4.5.33E: Find the derivative of the function.y = log 1 ? x
 4.5.34E: Find the derivative of the function.y = log3x
 4.5.35E: Find the derivative of the function.
 4.5.36E: Find the derivative of the function.
 4.5.37E: Find the derivative of the function.y = log3(x2 + 2x)3/2
 4.5.38E: Find the derivative of the function.y = log2(2x2 ? x)5/2
 4.5.39E: Find the derivative of the function.w = log8(2p ? 1)
 4.5.40E: Find the derivative of the function.z =10y log y
 4.5.41E: Find the derivative of the function.
 4.5.42E: Find the derivative of the function.
 4.5.43E: Find the derivative of the function.
 4.5.44E: Find the derivative of the function.
 4.5.45E: Why do we use the absolute value of x or of g(x) in the derivative ...
 4.5.46E: Prove ln x for any constant a.
 4.5.47E: A friend concludes that because y =ln 6x and y =ln x have the same ...
 4.5.48E: Use a graphing calculator to sketch the graph of y = f(x + h) –f(x)...
 4.5.49E: Using the fact that use the chain rule and the formula for the deri...
 4.5.50E: Using the fact that use the chain rule and the formula for the deri...
 4.5.51E: Use graphical differentiation to verify that
 4.5.52E: Use the fact that d ln x/dx =1/x, as well as the changeofbase the...
 4.5.53E: Let a. Using the fact thatln [u(x)v(x)] = v(x) ln (x),use the chain...
 4.5.54E: Use the idea from Exercise 53 to find the derivative of the of the ...
 4.5.55E: Use the idea from Exerciseto find the derivative of the of the foll...
 4.5.56A: Profit If the total revenue received from the sale of x items is gi...
 4.5.57A: Revenue Suppose the demand function for q units of a certain item i...
 4.5.58A: Profit If the cost function in dollars for q units of the item in E...
 4.5.59A: Marginal Average Cost Suppose the cost in dollars to make x oboe re...
 4.5.60A: Body Surface Area There is a mathematical relationship between an i...
 4.5.61A: Bologna Sausage Scientists have developed a model to predict the gr...
 4.5.62A: Pronghorn Fawns The field metabolic rate (FMR), or the total energy...
 4.5.63A: Fruit Flies A study of the relation between the rate of reproductio...
 4.5.64A: Insect Mating Consider an experiment in which equal numbers of male...
 4.5.65A: Population Growth Suppose that the population of a certain collecti...
 4.5.66A: Poverty The passage of the Social Security Amendments of 1965 resul...
 4.5.67A: Richter Scale The Richter scale provides a measure of the magnitude...
 4.5.68A: Street Crossing Consider a child waiting at a street corner for a g...
Solutions for Chapter 4.5: Calculus with Applications 10th Edition
Full solutions for Calculus with Applications  10th Edition
ISBN: 9780321749000
Solutions for Chapter 4.5
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus with Applications , edition: 10. Calculus with Applications was written by and is associated to the ISBN: 9780321749000. Chapter 4.5 includes 68 full stepbystep solutions. Since 68 problems in chapter 4.5 have been answered, more than 26445 students have viewed full stepbystep solutions from this chapter.

Acute triangle
A triangle in which all angles measure less than 90°

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Aphelion
The farthest point from the Sun in a planet’s orbit

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Coordinate plane
See Cartesian coordinate system.

Direct variation
See Power function.

Direction vector for a line
A vector in the direction of a line in threedimensional space

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Imaginary axis
See Complex plane.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Length of a vector
See Magnitude of a vector.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Line graph
A graph of data in which consecutive data points are connected by line segments

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Real number
Any number that can be written as a decimal.

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Solve a system
To find all solutions of a system.

Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>