 13.3.1: Think About It In Exercises 14, use the graph of the surface to det...
 13.3.2: Think About It In Exercises 14, use the graph of the surface to det...
 13.3.3: Think About It In Exercises 14, use the graph of the surface to det...
 13.3.4: Think About It In Exercises 14, use the graph of the surface to det...
 13.3.5: In Exercises 5 8, explain whether or not the Quotient Rule should b...
 13.3.6: In Exercises 5 8, explain whether or not the Quotient Rule should b...
 13.3.7: In Exercises 5 8, explain whether or not the Quotient Rule should b...
 13.3.8: In Exercises 5 8, explain whether or not the Quotient Rule should b...
 13.3.9: In Exercises 940, find both first partial derivativesx, y 2x 5y 3
 13.3.10: In Exercises 940, find both first partial derivatives
 13.3.11: In Exercises 940, find both first partial derivativesfx, y x2y3
 13.3.12: In Exercises 940, find both first partial derivatives
 13.3.13: In Exercises 940, find both first partial derivativesz xy
 13.3.14: In Exercises 940, find both first partial derivatives 2y z xy 2x
 13.3.15: In Exercises 940, find both first partial derivatives
 13.3.16: In Exercises 940, find both first partial derivativesz y3 2xy z x 2 1
 13.3.17: In Exercises 940, find both first partial derivativesz exy
 13.3.18: In Exercises 940, find both first partial derivativesz exy
 13.3.19: In Exercises 940, find both first partial derivativesz x2e2y
 13.3.20: In Exercises 940, find both first partial derivativesz yeyx
 13.3.21: In Exercises 940, find both first partial derivativesz ln z lnxy xy
 13.3.22: In Exercises 940, find both first partial derivatives
 13.3.23: In Exercises 940, find both first partial derivatives
 13.3.24: In Exercises 940, find both first partial derivativesz ln x yx y
 13.3.25: In Exercises 940, find both first partial derivatives
 13.3.26: In Exercises 940, find both first partial derivatives
 13.3.27: In Exercises 940, find both first partial derivativeshx, y ex2y2
 13.3.28: In Exercises 940, find both first partial derivativesgx, y ln x2 y 2
 13.3.29: In Exercises 940, find both first partial derivativesfx, y x2 y 2
 13.3.30: In Exercises 940, find both first partial derivatives
 13.3.31: In Exercises 940, find both first partial derivatives
 13.3.32: In Exercises 940, find both first partial derivativesz sinx 2y
 13.3.33: In Exercises 940, find both first partial derivativesz tan2x y
 13.3.34: In Exercises 940, find both first partial derivatives sin 5x cos 5y
 13.3.35: In Exercises 940, find both first partial derivativesz e y sin xy
 13.3.36: In Exercises 940, find both first partial derivativesz cosx2 y 2 z e
 13.3.37: In Exercises 940, find both first partial derivativesz sinh2x 3y
 13.3.38: In Exercises 940, find both first partial derivativesz cosh xy2
 13.3.39: In Exercises 940, find both first partial derivativesfx, y yxt 2 1 dt
 13.3.40: In Exercises 940, find both first partial derivativesfx, y yx2t 1 d...
 13.3.41: In Exercises 4144, use the limit definition of partial derivatives ...
 13.3.42: In Exercises 4144, use the limit definition of partial derivatives ...
 13.3.43: In Exercises 4144, use the limit definition of partial derivatives ...
 13.3.44: In Exercises 4144, use the limit definition of partial derivatives ...
 13.3.45: In Exercises 4552, evaluate and at the given point.fx, y ey sin x, , 0
 13.3.46: In Exercises 4552, evaluate and at the given point.
 13.3.47: In Exercises 4552, evaluate and at the given point.fx, y cos2x y, 4,3
 13.3.48: In Exercises 4552, evaluate and at the given point.fx, y sin xy, 2, 4
 13.3.49: In Exercises 4552, evaluate and at the given point.x, y arctan 2, 2
 13.3.50: In Exercises 4552, evaluate and at the given point.
 13.3.51: In Exercises 4552, evaluate and at the given point.fx, y 2, 2 xyx y
 13.3.52: In Exercises 4552, evaluate and at the given point.fx, y 1, 1 2xy4x...
 13.3.53: In Exercises 53 and 54, find the slopes of the surface in the  and...
 13.3.54: In Exercises 53 and 54, find the slopes of the surface in the  and...
 13.3.55: In Exercises 5558, use a computer algebra system to graph the curve...
 13.3.56: In Exercises 5558, use a computer algebra system to graph the curve...
 13.3.57: In Exercises 5558, use a computer algebra system to graph the curve...
 13.3.58: In Exercises 5558, use a computer algebra system to graph the curve...
 13.3.59: In Exercises 5964, find the first partial derivatives with respect ...
 13.3.60: In Exercises 5964, find the first partial derivatives with respect ...
 13.3.61: In Exercises 5964, find the first partial derivatives with respect ...
 13.3.62: In Exercises 5964, find the first partial derivatives with respect ...
 13.3.63: In Exercises 5964, find the first partial derivatives with respect ...
 13.3.64: In Exercises 5964, find the first partial derivatives with respect ...
 13.3.65: In Exercises 6570, evaluate and at the given point.fx, y, z x3yz2, ...
 13.3.66: In Exercises 6570, evaluate and at the given point.fx, y, z x 2, 1,...
 13.3.67: In Exercises 6570, evaluate and at the given point.
 13.3.68: In Exercises 6570, evaluate and at the given point.fx, y, z 3, 1, 1...
 13.3.69: In Exercises 6570, evaluate and at the given point.fx, y, z z sinx ...
 13.3.70: In Exercises 6570, evaluate and at the given point.fx, y, z 3x 1, 2...
 13.3.71: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.72: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.73: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.74: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.75: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.76: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.77: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.78: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.79: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.80: In Exercises 7180, find the four second partial derivatives. Observ...
 13.3.81: In Exercises 8188, for find all values of and such that and simulta...
 13.3.82: In Exercises 8188, for find all values of and such that and simulta...
 13.3.83: In Exercises 8188, for find all values of and such that and simulta...
 13.3.84: In Exercises 8188, for find all values of and such that and simulta...
 13.3.85: In Exercises 8188, for find all values of and such that and simulta...
 13.3.86: In Exercises 8188, for find all values of and such that and simulta...
 13.3.87: In Exercises 8188, for find all values of and such that and simulta...
 13.3.88: In Exercises 8188, for find all values of and such that and simulta...
 13.3.89: In Exercises 8992, use a computer algebra system to find the first ...
 13.3.90: In Exercises 8992, use a computer algebra system to find the first ...
 13.3.91: In Exercises 8992, use a computer algebra system to find the first ...
 13.3.92: In Exercises 8992, use a computer algebra system to find the first ...
 13.3.93: In Exercises 9396, show that the mixed partial derivatives and are ...
 13.3.94: In Exercises 9396, show that the mixed partial derivatives and are ...
 13.3.95: In Exercises 9396, show that the mixed partial derivatives and are ...
 13.3.96: In Exercises 9396, show that the mixed partial derivatives and are ...
 13.3.97: Laplaces Equation In Exercises 97100, show that the function satisf...
 13.3.98: Laplaces Equation In Exercises 97100, show that the function satisf...
 13.3.99: Laplaces Equation In Exercises 97100, show that the function satisf...
 13.3.100: Laplaces Equation In Exercises 97100, show that the function satisf...
 13.3.101: Wave Equation In Exercises 101104, show that the function satisfies...
 13.3.102: Wave Equation In Exercises 101104, show that the function satisfies...
 13.3.103: Wave Equation In Exercises 101104, show that the function satisfies...
 13.3.104: Wave Equation In Exercises 101104, show that the function satisfies...
 13.3.105: Heat Equation In Exercises 105 and 106, show that the function sati...
 13.3.106: Heat Equation In Exercises 105 and 106, show that the function sati...
 13.3.107: In Exercises 107 and 108, determine whether or not there exists a f...
 13.3.108: In Exercises 107 and 108, determine whether or not there exists a f...
 13.3.109: In Exercises 109 and 110, find the first partial derivative with re...
 13.3.110: In Exercises 109 and 110, find the first partial derivative with re...
 13.3.111: Let be a function of two variables and Describe the procedure for f...
 13.3.112: Sketch a surface representing a function of two variables and Use t...
 13.3.113: Sketch the graph of a function whose derivative is always negative ...
 13.3.114: Sketch the graph of a function whose derivatives and are always pos...
 13.3.115: If is a function of and such that and are continuous, what is the r...
 13.3.116: Find the four second partial derivatives of the function given by S...
 13.3.117: Marginal Revenue A pharmaceutical corporation has two plants that p...
 13.3.118: Marginal Costs A company manufactures two types of woodburning sto...
 13.3.119: Psychology Early in the twentieth century, an intelligence test cal...
 13.3.120: Marginal Productivity Consider the CobbDouglas production function...
 13.3.121: Think About It Let be the number of applicants to a university, the...
 13.3.122: Investment The value of an investment of $1000 earning 6% compounde...
 13.3.123: Temperature Distribution The temperature at any point in a steel pl...
 13.3.124: Apparent Temperature A measure of how hot weather feels to an avera...
 13.3.125: Ideal Gas Law The Ideal Gas Law states that where is pressure, is v...
 13.3.126: Marginal Utility The utility function is a measure of the utility (...
 13.3.127: Modeling Data Per capita consumptions (in gallons) of different typ...
 13.3.128: Modeling Data The table shows the public medical expenditures (in b...
 13.3.129: True or False? In Exercises 129132, determine whether the statement...
 13.3.130: True or False? In Exercises 129132, determine whether the statement...
 13.3.131: True or False? In Exercises 129132, determine whether the statement...
 13.3.132: True or False? In Exercises 129132, determine whether the statement...
 13.3.133: Consider the function defined by (a) Find and for (b) Use the defin...
 13.3.134: Let Find and x, yyx1 t3 dt
 13.3.135: Consider the function (a) Find and (b) Determine the points (if any...
 13.3.136: Consider the function Show that fxx, y 4x3x2 y213,0,x, y 0, 0x, y 0, 0
Solutions for Chapter 13.3: Partial Derivatives
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 13.3: Partial Derivatives
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. Since 136 problems in chapter 13.3: Partial Derivatives have been answered, more than 61093 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780547167022. Chapter 13.3: Partial Derivatives includes 136 full stepbystep solutions.

Absolute value of a vector
See Magnitude of a vector.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Arccosine function
See Inverse cosine function.

Bar chart
A rectangular graphical display of categorical data.

Divisor of a polynomial
See Division algorithm for polynomials.

Domain of a function
The set of all input values for a function

Equilibrium price
See Equilibrium point.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Limit to growth
See Logistic growth function.

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Quartic regression
A procedure for fitting a quartic function to a set of data.

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.

Series
A finite or infinite sum of terms.

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

Solve a system
To find all solutions of a system.

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

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.