 3.3.1: If f(x) = x2(x3 + 5), find f(x) two ways: by usingthe product rule ...
 3.3.2: If f(x)=2x 3x, find f(x) two ways: by using theproduct rule and by ...
 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 quotientrule to estimat...
 3.3.32: In 3133, use Figure 3.14 and the product or quotientrule to estimat...
 3.3.33: In 3133, use Figure 3.14 and the product or quotientrule to estimat...
 3.3.34: For 3439, let h(x) = f(x) g(x), and k(x) =f(x)/g(x), and l(x) = g(x...
 3.3.35: For 3439, let h(x) = f(x) g(x), and k(x) =f(x)/g(x), and l(x) = g(x...
 3.3.36: For 3439, let h(x) = f(x) g(x), and k(x) =f(x)/g(x), and l(x) = g(x...
 3.3.37: For 3439, let h(x) = f(x) g(x), and k(x) =f(x)/g(x), and l(x) = g(x...
 3.3.38: For 3439, let h(x) = f(x) g(x), and k(x) =f(x)/g(x), and l(x) = g(x...
 3.3.39: For 3439, let h(x) = f(x) g(x), and k(x) =f(x)/g(x), and l(x) = g(x...
 3.3.40: Differentiate f(t) = et by writing it as f(t) = 1et .
 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 e2xand using th...
 3.3.43: For what intervals is f(x) = xex concave up?
 3.3.44: For what intervals is g(x) = 1x2 + 1concave down?
 3.3.45: Find the equation of the tangent line to the graph off(x) = 2x 5x +...
 3.3.46: Find the equation of the tangent line at x = 1 to y =f(x) where f(x...
 3.3.47: (a) Differentiate y = exx , y = exx2 , and y = exx3 .(b) What do yo...
 3.3.48: In 4851, the functions f(x), g(x), and h(x) aredifferentiable for a...
 3.3.49: In 4851, the functions f(x), g(x), and h(x) aredifferentiable for a...
 3.3.50: In 4851, the functions f(x), g(x), and h(x) aredifferentiable for a...
 3.3.51: In 4851, the functions f(x), g(x), and h(x) aredifferentiable for a...
 3.3.52: Suppose f and g are differentiable functions with the valuesshown i...
 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) = 12 , and g(3) = 43 .Evaluate the fo...
 3.3.55: Find a possible formula for a function y = f(x) suchthat f(x) = 10x...
 3.3.56: The quantity, q, of a certain skateboard sold depends onthe selling...
 3.3.57: When an electric current passes through two resistorswith resistanc...
 3.3.58: A museum has decided to sell one of its paintings andto invest the ...
 3.3.59: Let f(v) be the gas consumption (in liters/km) of a cargoing at vel...
 3.3.60: The function f(x) = ex has the propertiesf(x) = f(x) and f(0) = 1.E...
 3.3.61: Find f(x) for the following functions with the productrule, rather ...
 3.3.62: Use the answer from to guess f(x) for thefollowing function:f(x)=(x...
 3.3.63: (a) Provide a threedimensional analogue for the geometricaldemonst...
 3.3.64: If P(x)=(x a)2Q(x), where Q(x) is a polynomialand Q(a) = 0, we call...
 3.3.65: Find and simplify d2dx2 (f(x)g(x)).
 3.3.66: In 6668, explain what is wrong with the statement.The derivative of...
 3.3.67: In 6668, explain what is wrong with the statement.Differentiating f...
 3.3.68: In 6668, explain what is wrong with the statement.The quotient f(x)...
 3.3.69: In 6970, give an example of:A function involving a sine and an expo...
 3.3.70: In 6970, give an example of:A function f(x) that can be differentia...
 3.3.71: Are the statements in 7173 true or false? Give anexplanation for yo...
 3.3.72: Are the statements in 7173 true or false? Give anexplanation for yo...
 3.3.73: Are the statements in 7173 true or false? Give anexplanation for yo...
 3.3.74: Which of the following would be a counterexample to theproduct rule...
Solutions for Chapter 3.3: THE PRODUCT AND QUOTIENT RULES
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 3.3: THE PRODUCT AND QUOTIENT RULES
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Chapter 3.3: THE PRODUCT AND QUOTIENT RULES includes 74 full stepbystep solutions. Since 74 problems in chapter 3.3: THE PRODUCT AND QUOTIENT RULES have been answered, more than 44947 students have viewed full stepbystep solutions from this chapter. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Direction of an arrow
The angle the arrow makes with the positive xaxis

Division
a b = aa 1 b b, b Z 0

Divisor of a polynomial
See Division algorithm for polynomials.

Elements of a matrix
See Matrix element.

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Interval
Connected subset of the real number line with at least two points, p. 4.

Limit to growth
See Logistic growth function.

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Open interval
An interval that does not include its endpoints.

Parametric curve
The graph of parametric equations.

Partial sums
See Sequence of partial sums.

Radicand
See Radical.

Righthand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.

Sequence
See Finite sequence, Infinite sequence.

Standard representation of a vector
A representative arrow with its initial point at the origin

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.