 11.1: Find and sketch the domain of the function.
 11.2: Find and sketch the domain of the function.
 11.3: Sketch the graph of the function
 11.4: Sketch the graph of the function
 11.5: Sketch several level curves of the function.
 11.6: Sketch several level curves of the function.
 11.7: Make a rough sketch of a contour map for the function whose graph i...
 11.8: A contour map of a function is shown. Use it to make a rough sketch...
 11.9: Evaluate the limit or show that it does not exist.
 11.10: Evaluate the limit or show that it does not exist.
 11.11: Find the first partial derivatives.
 11.12: Find the first partial derivatives.
 11.13: Find the first partial derivatives.
 11.14: Find the first partial derivatives.
 11.15: Find the first partial derivatives.
 11.16: The speed of sound traveling through ocean water is a function of t...
 11.17: Find all second partial derivatives of .
 11.18: Find all second partial derivatives of .
 11.19: Find all second partial derivatives of .
 11.20: Find all second partial derivatives of .
 11.21: If , show that
 11.22: If , show that
 11.23: Find equations of (a) the tangent plane and (b) the normal line to ...
 11.24: Find equations of (a) the tangent plane and (b) the normal line to ...
 11.25: Find equations of (a) the tangent plane and (b) the normal line to ...
 11.26: Find equations of (a) the tangent plane and (b) the normal line to ...
 11.27: Find equations of (a) the tangent plane and (b) the normal line to ...
 11.28: Use a computer to graph the surface and its tangent plane and norma...
 11.29: Find the points on the hyperboloid where the tangent plane is paral...
 11.31: Find the linear approximation of the function at the point (2, 3, 4...
 11.32: The two legs of a right triangle are measured as 5 m and 12 m with ...
 11.33: If , where , , and , use the Chain Rule to find
 11.34: . If , where and , use the Chain Rule to find and when and
 11.35: Suppose , where , , , , , , , , , and . Find and when and
 11.36: Use a tree diagram to write out the Chain Rule for the case where ,...
 11.37: If , where is differentiable, show that
 11.38: The length of a side of a triangle is increasing at a rate of 3 ins...
 11.39: If , where , , and has continuous second partial derivatives, show ...
 11.41: Find the gradient of the function
 11.42: (a) When is the directional derivative of a maximum? (b) When is it...
 11.43: Find the directional derivative of at the given point in the indica...
 11.44: Find the directional derivative of at the given point in the indica...
 11.45: Find the maximum rate of change of at the point . In which directio...
 11.46: Find parametric equations of the tangent line at the point to the c...
 11.47: Find the local maximum and minimum values and saddle points of the ...
 11.48: Find the local maximum and minimum values and saddle points of the ...
 11.49: Find the local maximum and minimum values and saddle points of the ...
 11.50: Find the local maximum and minimum values and saddle points of the ...
 11.51: Find the absolute maximum and minimum values of on the se
 11.52: Find the absolute maximum and minimum values of on the se
 11.53: Use a graph or level curves or both to estimate the local maximum a...
 11.54: Use a graphing calculator or computer (or Newtons method or a compu...
 11.55: Use Lagrange multipliers to find the maximum and minimum values of ...
 11.56: Use Lagrange multipliers to find the maximum and minimum values of ...
 11.57: Use Lagrange multipliers to find the maximum and minimum values of ...
 11.58: Use Lagrange multipliers to find the maximum and minimum values of ...
 11.59: Find the points on the surface that are closest to the origin.
 11.60: A package in the shape of a rectangular box can be mailed by the US...
 11.61: A pentagon is formed by placing an isosceles triangle on a rectangl...
 11.62: A particle of mass moves on the surface . Let and be the  and coo...
Solutions for Chapter 11: Partial Derivatives
Full solutions for Essential Calculus  2nd Edition
ISBN: 9781133112297
Solutions for Chapter 11: Partial Derivatives
Get Full SolutionsSummary of Chapter 11: Partial Derivatives
So far we have dealt with the calculus of functions of a single variable. But, in the real world, physical quantities often depend on two or more variables, so in this chapter we turn our attention to functions of several variables and extend the basic ideas of differential calculus to such functions.
Essential Calculus was written by and is associated to the ISBN: 9781133112297. Since 60 problems in chapter 11: Partial Derivatives have been answered, more than 26551 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11: Partial Derivatives includes 60 full stepbystep solutions.

Confounding variable
A third variable that affects either of two variables being studied, making inferences about causation unreliable

Differentiable at x = a
ƒ'(a) exists

Feasible points
Points that satisfy the constraints in a linear programming problem.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Inverse cosine function
The function y = cos1 x

Logistic regression
A procedure for fitting a logistic curve to a set of data

Modified boxplot
A boxplot with the outliers removed.

Natural numbers
The numbers 1, 2, 3, . . . ,.

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.

Regression model
An equation found by regression and which can be used to predict unknown values.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Right triangle
A triangle with a 90° angle.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Slopeintercept form (of a line)
y = mx + b

Speed
The magnitude of the velocity vector, given by distance/time.

Terminal side of an angle
See Angle.

Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.

Unit vector
Vector of length 1.

Vertex of a cone
See Right circular cone.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].