 12.5.25E: Making trees Use a tree diagram to write the required Chain Rule fo...
 12.5.26E: Making trees Use a tree diagram to write the required Chain Rule fo...
 12.5.36E: Derivative practice two ways Find the indicated derivative in two w...
 12.5.37E: Derivative practice two ways Find the indicated derivative in two w...
 12.5.16E: Changing pyramid The volume of a pyramid with a square base x units...
 12.5.13E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.38E: Derivative practice Find the indicated derivative for the following...
 12.5.53E: Conservation of energy A projectile with mass m is launched into th...
 12.5.62AE: Geometry of implicit differentiation Suppose x and y are related by...
 12.5.65AE: Subtleties of the Chain Rule Let w = f(x, y, z) = 2x+ 3y +4z, which...
 12.5.33E: Fluid flow The x and ycomponents of a fluid moving in two dimensi...
 12.5.29E: Implicit differentiation Given the following equations, evaluate dy...
 12.5.12E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.10E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.49E: Walking on a surface Consider the following surfaces specified in t...
 12.5.31E: Implicit differentiation Given the following equations, evaluate dy...
 12.5.60AE: Change of coordinates Recall that Cartesian and polar coordinates a...
 12.5.21E: Chain Rule with several independent variables Find the following de...
 12.5.8E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.59E: Spiral through a domain Suppose you follow the spiral pathC: x =cos...
 12.5.6E: Suppose F(x, y) = 0 and y is a differentiable function of x. Explai...
 12.5.9E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.54E: Utility functions in economics Economists use utility functions to ...
 12.5.64AE: Second derivative Let f(x, y) = 0 define y as a twice differentiab...
 12.5.22E: Chain Rule with several independent variables Find the following de...
 12.5.5E: Given that w = F(x, y, z), and x, y, and z are functions of r and s...
 12.5.15E: Changing cylinder The volume of a right circular cylinder with radi...
 12.5.39E: Derivative practice Find the indicated derivative for the following...
 12.5.14E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.58E: Variable density The density of a thin circular plate of radius 2 i...
 12.5.61AE: Change of coordinates continued An important derivative operation ...
 12.5.32E: Implicit differentiation Given the following equations, evaluate dy...
 12.5.4E: Let z = f(x, y), x = g(s, t), and y = h(s, t). Explain how to find ...
 12.5.63AE: General threevariable relationship In the implicit relationship f(...
 12.5.56E: Body surface area One of several empirical formulas that relates th...
 12.5.30E: Implicit differentiation Given the following equations, evaluate dy...
 12.5.34E: Fluid flow The x and ycomponents of a fluid moving in two dimensi...
 12.5.28E: Implicit differentiation Given the following equations, evaluate dy...
 12.5.40E: Derivative practice Find the indicated derivative for the following...
 12.5.23E: Making trees Use a tree diagram to write the required Chain Rule fo...
 12.5.42E: Derivative practice Find the indicated derivative for the following...
 12.5.48E: More than one way Let exyz = 2. Find zx and zy in three ways (and c...
 12.5.57E: The Ideal Gas Law The pressure, temperature, and volume of an ideal...
 12.5.43E: Change on a line Suppose w = f(x, y, z) and ? is the liner(t) = ?at...
 12.5.27E: Implicit differentiation Given the following equations, evaluate dy...
 12.5.45E: Implicit differentiation with three variables Use the result of Exe...
 12.5.47E: Implicit differentiation with three variables Use the result of Exe...
 12.5.55E: Constant volume tori The volume of a solid torus is given by V = (?...
 12.5.3E: Suppose w is a function of x, y, and z, which are the functions of ...
 12.5.41E: Derivative practice Find the indicated derivative for the following...
 12.5.50E: Walking on a surface Consider the following surfaces specified in t...
 12.5.46E: Implicit differentiation with three variables Use the result of Exe...
 12.5.11E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.51E: Walking on a surface Consider the following surfaces specified in t...
 12.5.7E: Chain Rule with one independent variable Use Theorem 12.7 to find t...
 12.5.35E: Explain why or why not Determine whether the following statements a...
 12.5.1E: Suppose z = f(x,y), where x and y are functions of t. How many depe...
 12.5.2E: Let z be a function of x and y, while x and y are functions of t. E...
 12.5.44E: Implicit differentiation rule with three variables Assume thatF(x, ...
 12.5.18E: Chain Rule with several independent variables Find the following de...
 12.5.19E: Chain Rule with several independent variables Find the following de...
 12.5.17E: Chain Rule with several independent variables Find the following de...
 12.5.52E: Walking on a surface Consider the following surfaces specified in t...
 12.5.20E: Chain Rule with several independent variables Find the following de...
 12.5.24E: Making trees Use a tree diagram to write the required Chain Rule fo...
Solutions for Chapter 12.5: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 12.5
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since 65 problems in chapter 12.5 have been answered, more than 141639 students have viewed full stepbystep solutions from this chapter. Chapter 12.5 includes 65 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions.

Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point

Annual percentage rate (APR)
The annual interest rate

Demand curve
p = g(x), where x represents demand and p represents price

Directed line segment
See Arrow.

Focus, foci
See Ellipse, Hyperbola, Parabola.

Inductive step
See Mathematical induction.

Limit to growth
See Logistic growth function.

Line of travel
The path along which an object travels

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Mean (of a set of data)
The sum of all the data divided by the total number of items

Partial sums
See Sequence of partial sums.

Principle of mathematical induction
A principle related to mathematical induction.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.

Second
Angle measure equal to 1/60 of a minute.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Variation
See Power function.

Zero of a function
A value in the domain of a function that makes the function value zero.