 2.3.1: In Exercises 19, calculate f/x and f/y.(x, y) = x y2 + x 2 y
 2.3.2: In Exercises 19, calculate f/x and f/y.f (x, y) = ex2+y2
 2.3.3: In Exercises 19, calculate f/x and f/y.f (x, y) = sin x y + cos x y
 2.3.4: In Exercises 19, calculate f/x and f/y.f (x, y) = x 3 y2 1 + x 2 + 3y4
 2.3.5: In Exercises 19, calculate f/x and f/y.f (x, y) = x 2 y2 x 2 + y2
 2.3.6: In Exercises 19, calculate f/x and f/y.f (x, y) = ln (x 2 + y2)
 2.3.7: In Exercises 19, calculate f/x and f/y.f (x, y) = cos x 3 y
 2.3.8: In Exercises 19, calculate f/x and f/y.f (x, y) = ln x y
 2.3.9: In Exercises 19, calculate f/x and f/y.f (x, y) = xey + y sin (x 2 ...
 2.3.10: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.11: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.12: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.13: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.14: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.15: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.16: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.17: In Exercises 1017, evaluate the partial derivatives F/x, F/y, and F...
 2.3.18: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.19: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.20: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.21: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.22: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.23: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.24: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.25: Find the gradient f (a), where f and a are given in Exercises 1825....
 2.3.26: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.27: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.28: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.29: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.30: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.31: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.32: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.33: In Exercises 2633, find the matrix Df(a) of partial derivatives, wh...
 2.3.34: Explain why each of the functions given in Exercises 3436 is differ...
 2.3.35: Explain why each of the functions given in Exercises 3436 is differ...
 2.3.36: Explain why each of the functions given in Exercises 3436 is differ...
 2.3.37: (a) Explain why the graph of z = x 3 7x y + ey has a tangent plane ...
 2.3.38: Find an equation for the plane tangent to the graph of z = 4 cos x ...
 2.3.39: Find an equation for the plane tangent to the graph of z = ex+y cos...
 2.3.40: Find equations for the planes tangent to z = x 2 6x + y3 that are p...
 2.3.41: Use formula (8) to find an equation for the hyperplane tangent to t...
 2.3.42: Suppose that you have the following information concerning a differ...
 2.3.43: In Exercises 4345, (a) use the linear function h(x) in Definition 3...
 2.3.44: In Exercises 4345, (a) use the linear function h(x) in Definition 3...
 2.3.45: In Exercises 4345, (a) use the linear function h(x) in Definition 3...
 2.3.46: Calculate the partial derivatives of f (x1, x2,..., xn) = x1 + x2 +...
 2.3.47: As mentioned in the text, if a function F(x) of a single variable i...
 2.3.48: As mentioned in the text, if a function F(x) of a single variable i...
 2.3.49: As mentioned in the text, if a function F(x) of a single variable i...
 2.3.50: As mentioned in the text, if a function F(x) of a single variable i...
 2.3.51: As mentioned in the text, if a function F(x) of a single variable i...
 2.3.52: (a) Use a computer to graph the function F(x) = (x 2)2/3. (b) By zo...
 2.3.53: As discussed in the text, a function f (x, y) may have partial deri...
 2.3.54: As discussed in the text, a function f (x, y) may have partial deri...
 2.3.55: As discussed in the text, a function f (x, y) may have partial deri...
 2.3.56: As discussed in the text, a function f (x, y) may have partial deri...
 2.3.57: As discussed in the text, a function f (x, y) may have partial deri...
 2.3.58: Let g(x, y) = 3 x y. (a) Is g continuous at (0, 0)? (b) Calculate g...
 2.3.59: Suppose f: Rn Rm is a linear mapping; that is, f(x) = Ax, where x =...
 2.3.60: In Exercises 6062 you will establish that the matrix Df(a) of parti...
 2.3.61: In Exercises 6062 you will establish that the matrix Df(a) of parti...
 2.3.62: In Exercises 6062 you will establish that the matrix Df(a) of parti...
Solutions for Chapter 2.3: The Derivative
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 2.3: The Derivative
Get Full SolutionsSince 62 problems in chapter 2.3: The Derivative have been answered, more than 12422 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Chapter 2.3: The Derivative includes 62 full stepbystep solutions.

Additive inverse of a real number
The opposite of b , or b

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Common logarithm
A logarithm with base 10.

Cotangent
The function y = cot x

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Exponent
See nth power of a.

Imaginary part of a complex number
See Complex number.

Negative linear correlation
See Linear correlation.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Orthogonal vectors
Two vectors u and v with u x v = 0.

Outcomes
The various possible results of an experiment.

Parameter interval
See Parametric equations.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Positive angle
Angle generated by a counterclockwise rotation.

Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02

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.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Unit ratio
See Conversion factor.

Vertical line
x = a.