 14.3.1: The temperature (in at a location in the Northern Hemisphere depend...
 14.3.2: At the beginning of this section we discussed the function , where ...
 14.3.3: The windchill index is the perceived temperature when the actual t...
 14.3.4: The wave heights in the open sea depend on the speed of the wind an...
 14.3.5: Determine the signs of the partial derivatives for the function who...
 14.3.6: Determine the signs of the partial derivatives for the function who...
 14.3.7: Determine the signs of the partial derivatives for the function who...
 14.3.8: Determine the signs of the partial derivatives for the function who...
 14.3.9: The following surfaces, labeled , , and , are graphs of a function ...
 14.3.10: A contour map is given for a function . Use it to estimate and .
 14.3.11: If , find and and interpret these numbers as slopes. Illustrate wit...
 14.3.12: If , find and and interpret these numbers as slopes. Illustrate wit...
 14.3.13: Find and and graph , , and with domains and viewpoints that enable ...
 14.3.14: Find and and graph , , and with domains and viewpoints that enable ...
 14.3.15: Find the first partial derivatives of the function.
 14.3.16: Find the first partial derivatives of the function.
 14.3.17: Find the first partial derivatives of the function.
 14.3.18: Find the first partial derivatives of the function.
 14.3.19: Find the first partial derivatives of the function.
 14.3.20: Find the first partial derivatives of the function.
 14.3.21: Find the first partial derivatives of the function.
 14.3.22: Find the first partial derivatives of the function.
 14.3.23: Find the first partial derivatives of the function.
 14.3.24: Find the first partial derivatives of the function.
 14.3.25: Find the first partial derivatives of the function.
 14.3.26: Find the first partial derivatives of the function.
 14.3.27: Find the first partial derivatives of the function.
 14.3.28: Find the first partial derivatives of the function.
 14.3.29: Find the first partial derivatives of the function.
 14.3.30: Find the first partial derivatives of the function.
 14.3.31: Find the first partial derivatives of the function.
 14.3.32: Find the first partial derivatives of the function.
 14.3.33: Find the first partial derivatives of the function.
 14.3.34: Find the first partial derivatives of the function.
 14.3.35: Find the first partial derivatives of the function.
 14.3.36: Find the first partial derivatives of the function.
 14.3.37: Find the first partial derivatives of the function.
 14.3.38: Find the first partial derivatives of the function.
 14.3.39: Find the first partial derivatives of the function.
 14.3.40: Find the first partial derivatives of the function.
 14.3.41: Find the indicated partial derivative.
 14.3.42: Find the indicated partial derivative.
 14.3.43: Find the indicated partial derivative.
 14.3.44: Find the indicated partial derivative.
 14.3.45: Use the definition of partial derivatives as limits to find and .
 14.3.46: Use the definition of partial derivatives as limits to find and .
 14.3.47: Use implicit differentiation to find and .
 14.3.48: Use implicit differentiation to find and .
 14.3.49: Use implicit differentiation to find and .
 14.3.50: Use implicit differentiation to find and .
 14.3.51: Find zx and zy.
 14.3.52: Find zx and zy.
 14.3.53: Find all the second partial derivatives
 14.3.54: Find all the second partial derivatives
 14.3.55: Find all the second partial derivatives
 14.3.56: Find all the second partial derivatives
 14.3.57: Find all the second partial derivatives
 14.3.58: Find all the second partial derivatives
 14.3.59: Verify that the conclusion of Clairauts Theorem holds, that is, .
 14.3.60: Verify that the conclusion of Clairauts Theorem holds, that is, .
 14.3.61: Verify that the conclusion of Clairauts Theorem holds, that is, .
 14.3.62: Verify that the conclusion of Clairauts Theorem holds, that is, .
 14.3.63: Find the indicated partial derivative(s).
 14.3.64: Find the indicated partial derivative(s).
 14.3.65: Find the indicated partial derivative(s).
 14.3.66: Find the indicated partial derivative(s).
 14.3.67: Find the indicated partial derivative(s).
 14.3.68: Find the indicated partial derivative(s).
 14.3.69: Find the indicated partial derivative(s).
 14.3.70: Find the indicated partial derivative(s).
 14.3.71: If , find . [Hint: Which order of differentiation is easiest?]
 14.3.72: If , find . [Hint: Use a different order of differentiation for eac...
 14.3.73: Use the table of values of to estimate the values of , , and .
 14.3.74: Level curves are shown for a function . Determine whether the follo...
 14.3.75: Verify that the function is a solution of the heat conduction equat...
 14.3.76: Determine whether each of the following functions is a solution of ...
 14.3.77: Verify that the function is a solution of the threedimensional Lap...
 14.3.78: Show that each of the following functions is a solution of the wave...
 14.3.79: If and are twice differentiable functions of a single variable, sho...
 14.3.80: If , where , show that
 14.3.81: Verify that the function is a solution of the differential equation...
 14.3.82: The temperature at a point on a flat metal plate is given by , wher...
 14.3.83: The total resistance produced by three conductors with resistances ...
 14.3.84: Show that the CobbDouglas production function satisfies the equation
 14.3.85: Show that the CobbDouglas production function satisfies by solving...
 14.3.86: Cobb and Douglas used the equation to model the American economy fr...
 14.3.87: The van der Waals equation for moles of a gas is where is the press...
 14.3.88: The gas law for a fixed mass of an ideal gas at absolute temperatur...
 14.3.89: For the ideal gas of Exercise 88, show that
 14.3.90: The windchill index is modeled by the function where is the temper...
 14.3.91: The kinetic energy of a body with mass and velocity is . Show that
 14.3.92: If , , are the sides of a triangle and , , are the opposite angles,...
 14.3.93: You are told that there is a function whose partial derivatives are...
 14.3.94: The paraboloid intersects the plane in a parabola. Find parametric ...
 14.3.95: The ellipsoid intersects the plane in an ellipse. Find parametric e...
 14.3.96: In a study of frost penetration it was found that the temperature a...
 14.3.97: Use Clairauts Theorem to show that if the thirdorder partial deriv...
 14.3.98: (a) How many thorder partial derivatives does a function of two va...
 14.3.99: If , find . [Hint: Instead of finding first, note that its easier t...
 14.3.100: If , find .
 14.3.101: Let ; (a) Use a computer to graph . (b) Find and when . (c) Find an...
Solutions for Chapter 14.3: PARTIAL DERIVATIVES
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 14.3: PARTIAL DERIVATIVES
Get Full SolutionsSince 101 problems in chapter 14.3: PARTIAL DERIVATIVES have been answered, more than 23708 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. Chapter 14.3: PARTIAL DERIVATIVES includes 101 full stepbystep solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

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

Boundary
The set of points on the “edge” of a region

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Dependent event
An event whose probability depends on another event already occurring

DMS measure
The measure of an angle in degrees, minutes, and seconds

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Finite series
Sum of a finite number of terms.

Focal length of a parabola
The directed distance from the vertex to the focus.

Nappe
See Right circular cone.

Period
See Periodic function.

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Standard form of a complex number
a + bi, where a and b are real numbers

Statute mile
5280 feet.

Subtraction
a  b = a + (b)

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k

Vertical line
x = a.

Xscl
The scale of the tick marks on the xaxis in a viewing window.