 14.3.1: Patricia derived the following incorrect formula by misapplying the...
 14.3.2: Explain why it is not necessary to use the Quotient Rule to compute...
 14.3.3: Which of the following partial derivatives should be evaluated with...
 14.3.4: What is fx , where f (x, y, z) = (sin yz)ez3z1y ?
 14.3.5: Assuming the hypotheses of Clairauts Theorem are satisfied, which o...
 14.3.6: Explain the relation between the following two formulas (c is a con...
 14.3.7: The plane y = 1 intersects the surface z = x4 + 6xy y4 in a certain...
 14.3.8: Determine whether the partial derivatives f/x and f/y are positive ...
 14.3.9: In Exercises 912, refer to Figure 8. 9. Estimate fx and fy at point A.
 14.3.10: In Exercises 912, refer to Figure 8. 9. Estimate fx and fy at point A.
 14.3.11: Starting at point B, in which compass direction (N, NE, SW, etc.) d...
 14.3.12: At which of A, B, or C is fy smallest? x y 10 10 20 A B C 50 70 50 ...
 14.3.13: In Exercises 1340, compute the firstorder partial derivatives. 13....
 14.3.14: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.15: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.16: In Exercises 1340, compute the firstorder partial derivatives.V = r2h
 14.3.17: In Exercises 1340, compute the firstorder partial derivatives.z = x y
 14.3.18: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.19: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.20: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.21: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.22: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.23: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.24: In Exercises 1340, compute the firstorder partial derivatives.S = ...
 14.3.25: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.26: In Exercises 1340, compute the firstorder partial derivatives.A = ...
 14.3.27: In Exercises 1340, compute the firstorder partial derivatives.W = ...
 14.3.28: In Exercises 1340, compute the firstorder partial derivatives.Q = re
 14.3.29: In Exercises 1340, compute the firstorder partial derivatives.z = exy
 14.3.30: In Exercises 1340, compute the firstorder partial derivatives.R = ...
 14.3.31: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.32: In Exercises 1340, compute the firstorder partial derivatives.P = ...
 14.3.33: In Exercises 1340, compute the firstorder partial derivatives.U = ...
 14.3.34: In Exercises 1340, compute the firstorder partial derivatives.z = yx
 14.3.35: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.36: In Exercises 1340, compute the firstorder partial derivatives.z = ...
 14.3.37: In Exercises 1340, compute the firstorder partial derivatives.w = ...
 14.3.38: In Exercises 1340, compute the firstorder partial derivatives.w = ...
 14.3.39: In Exercises 1340, compute the firstorder partial derivatives.Q = ...
 14.3.40: In Exercises 1340, compute the firstorder partial derivatives.w = ...
 14.3.41: In Exercises 4144, compute the given partial derivatives. f (x, y) ...
 14.3.42: In Exercises 4144, compute the given partial derivatives. f (x, y) ...
 14.3.43: In Exercises 4144, compute the given partial derivatives. g(u, v) =...
 14.3.44: In Exercises 4144, compute the given partial derivatives. h(x,z) = ...
 14.3.45: Exercises 45 and 46 refer to Example 5. Calculate N for L = 0.4, R ...
 14.3.46: Exercises 45 and 46 refer to Example 5. Estimate N if (L, R, d) = (...
 14.3.47: The heat index I is a measure of how hot it feels when the relative...
 14.3.48: The windchill temperature W measures how cold people feel (based o...
 14.3.49: The volume of a rightcircular cone of radius r and height h is V =...
 14.3.50: Use the linear approximation to estimate the percentage change in v...
 14.3.51: Calculate W/E and W/T , where W = eE/kT , where k is a constant.
 14.3.52: Calculate P/T and P/V , where pressure P, volume V , and temperatur...
 14.3.53: Use the contour map of f (x, y) in Figure 9 to explain the followin...
 14.3.54: Estimate the partial derivatives at P of the function whose contour...
 14.3.55: Over most of the earth, a magnetic compass does not point to true (...
 14.3.56: Refer to Table 1. (a) Estimate /T and /S at the points (S, T ) = (3...
 14.3.57: In Exercises 5762, compute the derivatives indicated. 57. f (x, y) ...
 14.3.58: In Exercises 5762, compute the derivatives indicated.g(x, y) = xy x...
 14.3.59: In Exercises 5762, compute the derivatives indicated.h(u,v) = u u +...
 14.3.60: In Exercises 5762, compute the derivatives indicated.h(x, y) = ln(x...
 14.3.61: In Exercises 5762, compute the derivatives indicated.f (x, y) = x l...
 14.3.62: In Exercises 5762, compute the derivatives indicated.g(x, y) = xexy...
 14.3.63: Compute fxyxzy for f (x, y, z) = y sin(xz)sin(x + z) + (x + z2)tan ...
 14.3.64: Let f (x, y, u, v) = x2 + ey v 3y2 + ln(2 + u2) What is the fastest...
 14.3.65: In Exercises 6572, compute the derivative indicated. 65. f (u, v) =...
 14.3.66: In Exercises 6572, compute the derivative indicated.g(x, y, z) = x4...
 14.3.67: In Exercises 6572, compute the derivative indicated.F(r, s, t) = r(...
 14.3.68: In Exercises 6572, compute the derivative indicated.u(x,t) = t 1/2e...
 14.3.69: In Exercises 6572, compute the derivative indicated.F(, u, v) = sin...
 14.3.70: In Exercises 6572, compute the derivative indicated.R(u, v, w) = u ...
 14.3.71: In Exercises 6572, compute the derivative indicated.g(x, y, z) = x2...
 14.3.72: In Exercises 6572, compute the derivative indicated.u(x,t) = sech2(...
 14.3.73: Find a function such that f x = 2xy and f y = x2.
 14.3.74: Prove that there does not exist any function f (x, y) such that f x...
 14.3.75: Assume that fxy and fyx are continuous and that fyxx exists. Show t...
 14.3.76: Show that u(x,t) = sin(nx)en2t satisfies the heat equation for any ...
 14.3.77: Find all values of A and B such that f (x, t) = eAx+Bt satisfies Eq...
 14.3.78: The function f (x, t) = 1 2 t ex2/4t describes the temperature prof...
 14.3.79: The function f (x, t) = 1 2 t ex2/4t describes the temperature prof...
 14.3.80: Find all harmonic polynomials u(x, y) of degree 3, that is, u(x, y)...
 14.3.81: Show that if u(x, y)is harmonic, then the partial derivatives u/x a...
 14.3.82: Find all constants a,b such that u(x, y) = cos(ax)eby is harmonic.
 14.3.83: Show that u(x,t) = sech2(x t) satisfies the KortewegdeVries equatio...
 14.3.84: Assumptions Matter This exercise shows that the hypotheses of Clair...
Solutions for Chapter 14.3: Partial Derivatives
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 14.3: Partial Derivatives
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Since 84 problems in chapter 14.3: Partial Derivatives have been answered, more than 42037 students have viewed full stepbystep solutions from this chapter. Chapter 14.3: Partial Derivatives includes 84 full stepbystep solutions.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Categorical variable
In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Equation
A statement of equality between two expressions.

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

Gaussian curve
See Normal curve.

Index of summation
See Summation notation.

Instantaneous rate of change
See Derivative at x = a.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

Irrational zeros
Zeros of a function that are irrational numbers.

Negative numbers
Real numbers shown to the left of the origin on a number line.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Positive angle
Angle generated by a counterclockwise rotation.

Quotient polynomial
See Division algorithm for polynomials.

Reexpression of data
A transformation of a data set.

Solution set of an inequality
The set of all solutions of an inequality

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Translation
See Horizontal translation, Vertical translation.

xzplane
The points x, 0, z in Cartesian space.