 3.3.1: If f(x) = x2(x3 + 5), find f (x) two ways: by using the product rul...
 3.3.2: If f(x)=2x 3x, find f (x) two ways: by using the product rule and b...
 3.3.3: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.4: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.5: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.6: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.7: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.8: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.9: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.10: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.11: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.12: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.13: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.14: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.15: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.16: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.17: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.18: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.19: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.20: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.21: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.22: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.23: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.24: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.25: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.26: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.27: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.28: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.29: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.30: For Exercises 330, find the derivative. It may be to your advantage...
 3.3.31: In 3133, use Figure 3.14 and the product or quotient rule to estima...
 3.3.32: In 3133, use Figure 3.14 and the product or quotient rule to estima...
 3.3.33: In 3133, use Figure 3.14 and the product or quotient rule to estima...
 3.3.34: For 3439, let h(x) = f(x) g(x), and k(x) = f(x)/g(x), and l(x) = g(...
 3.3.35: For 3439, let h(x) = f(x) g(x), and k(x) = f(x)/g(x), and l(x) = g(...
 3.3.36: For 3439, let h(x) = f(x) g(x), and k(x) = f(x)/g(x), and l(x) = g(...
 3.3.37: For 3439, let h(x) = f(x) g(x), and k(x) = f(x)/g(x), and l(x) = g(...
 3.3.38: For 3439, let h(x) = f(x) g(x), and k(x) = f(x)/g(x), and l(x) = g(...
 3.3.39: For 3439, let h(x) = f(x) g(x), and k(x) = f(x)/g(x), and l(x) = g(...
 3.3.40: Differentiate f(t) = et by writing it as f(t) = 1 et
 3.3.41: Differentiate f(x) = e2x by writing it as f(x) = ex ex.
 3.3.42: Differentiate f(x) = e3x by writing it as f(x) = ex e2x and using t...
 3.3.43: For what intervals is f(x) = xex concave up?
 3.3.44: For what intervals is g(x) = 1 x2 + 1 concave down?
 3.3.45: Find the equation of the tangent line to the graph of f(x) = 2x 5 x...
 3.3.46: Find the equation of the tangent line at x = 1 to y = f(x) where f(...
 3.3.47: (a) Differentiate y = ex x , y = ex x2 , and y = ex x3 . (b) What d...
 3.3.48: In 4851, the functions f(x), g(x), and h(x) are differentiable for ...
 3.3.49: In 4851, the functions f(x), g(x), and h(x) are differentiable for ...
 3.3.50: In 4851, the functions f(x), g(x), and h(x) are differentiable for ...
 3.3.51: In 4851, the functions f(x), g(x), and h(x) are differentiable for ...
 3.3.52: Suppose f and g are differentiable functions with the values shown ...
 3.3.53: If H(3) = 1, H (3) = 3, F(3) = 5, F (3) = 4, find: (a) G (3) if G(z...
 3.3.54: Let f(3) = 6, g(3) = 12, f (3) = 1 2 , and g (3) = 4 3 . Evaluate t...
 3.3.55: Find a possible formula for a function y = f(x) such that f (x) = 1...
 3.3.56: The quantity, q, of a certain skateboard sold depends on the sellin...
 3.3.57: When an electric current passes through two resistors with resistan...
 3.3.58: A museum has decided to sell one of its paintings and to invest the...
 3.3.59: Let f(v) be the gas consumption (in liters/km) of a car going at ve...
 3.3.60: The function f(x) = ex has the properties f (x) = f(x) and f(0) = 1...
 3.3.61: Find f (x) for the following functions with the product rule, rathe...
 3.3.62: Use the answer from to guess f (x) for the following function: f(x)...
 3.3.63: (a) Provide a threedimensional analogue for the geometrical demons...
 3.3.64: (a) Provide a threedimensional analogue for the geometrical demons...
 3.3.65: Find and simplify d2 dx2 (f(x)g(x)).
 3.3.66: In 6668, explain what is wrong with the statement.
 3.3.67: In 6668, explain what is wrong with the statement.
 3.3.68: In 6668, explain what is wrong with the statement.
 3.3.69: A function involving a sine and an exponential that can be differen...
 3.3.70: A function f(x) that can be differentiated both using the product r...
 3.3.71: Are the statements in 7173 true or false? Give an explanation for y...
 3.3.72: If the function f(x)/g(x) is defined but not differentiable at x = ...
 3.3.73: Suppose that f and g exist and f and g are concave up for all x, th...
 3.3.74: Which of the following would be a counterexample to the product rul...
Solutions for Chapter 3.3: THE PRODUCT AND QUOTIENT RULES
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 3.3: THE PRODUCT AND QUOTIENT RULES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Since 74 problems in chapter 3.3: THE PRODUCT AND QUOTIENT RULES have been answered, more than 32451 students have viewed full stepbystep solutions from this chapter. Chapter 3.3: THE PRODUCT AND QUOTIENT RULES includes 74 full stepbystep solutions.

Addition property of equality
If u = v and w = z , then u + w = v + z

Arccosecant function
See Inverse cosecant function.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

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

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

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 of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Frequency table (in statistics)
A table showing frequencies.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Index
See Radical.

Inductive step
See Mathematical induction.

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Partial fraction decomposition
See Partial fractions.

Pie chart
See Circle graph.

Polar axis
See Polar coordinate system.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Solve a system
To find all solutions of a system.

Solve by substitution
Method for solving systems of linear equations.

Ymin
The yvalue of the bottom of the viewing window.