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# Solutions for Chapter 14.5: THE CHAIN RULE

## Full solutions for Multivariable Calculus, | 7th Edition

ISBN: 9780538497879

Solutions for Chapter 14.5: THE CHAIN RULE

Solutions for Chapter 14.5
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##### ISBN: 9780538497879

Since 59 problems in chapter 14.5: THE CHAIN RULE have been answered, more than 23588 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. Chapter 14.5: THE CHAIN RULE includes 59 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Binomial probability

In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once

• Bounded above

A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

• Complements or complementary angles

Two angles of positive measure whose sum is 90°

• Compounded annually

See Compounded k times per year.

• Compounded continuously

Interest compounded using the formula A = Pert

• Cube root

nth root, where n = 3 (see Principal nth root),

• Definite integral

The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

• Dot product

The number found when the corresponding components of two vectors are multiplied and then summed

• Focal length of a parabola

The directed distance from the vertex to the focus.

• Implied domain

The domain of a function’s algebraic expression.

• Increasing on an interval

A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

• Mapping

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

• Natural logarithmic function

The inverse of the exponential function y = ex, denoted by y = ln x.

• Negative association

A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

• Rational function

Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

• Recursively defined sequence

A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

• Statistic

A number that measures a quantitative variable for a sample from a population.

• Variation

See Power function.

• y-axis

Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.