 3.3.1: Are the following statements true or false? If false, state the cor...
 3.3.2: Find (f/g) (1) if f (1) = f (1) = g(1) = 2 and g (1) = 4.
 3.3.3: Find g(1) if f (1) = 0, f (1) = 2, and (fg) (1) = 10.
 3.3.4: In Exercises 16, use the Product Rule to calculate the derivative. ...
 3.3.5: In Exercises 16, use the Product Rule to calculate the derivative. ...
 3.3.6: In Exercises 16, use the Product Rule to calculate the derivative. ...
 3.3.7: In Exercises 712, use the Quotient Rule to calculate the derivative...
 3.3.8: In Exercises 712, use the Quotient Rule to calculate the derivative...
 3.3.9: In Exercises 712, use the Quotient Rule to calculate the derivative...
 3.3.10: In Exercises 712, use the Quotient Rule to calculate the derivative...
 3.3.11: In Exercises 712, use the Quotient Rule to calculate the derivative...
 3.3.12: In Exercises 712, use the Quotient Rule to calculate the derivative...
 3.3.13: In Exercises 1316, calculate the derivative in two ways. First use ...
 3.3.14: In Exercises 1316, calculate the derivative in two ways. First use ...
 3.3.15: In Exercises 1316, calculate the derivative in two ways. First use ...
 3.3.16: In Exercises 1316, calculate the derivative in two ways. First use ...
 3.3.17: In Exercises 1738, calculate the derivative. f (x) = (x3 + 5)(x3 + ...
 3.3.18: In Exercises 1738, calculate the derivative. x) = (4ex x2)(x3 + 1)
 3.3.19: In Exercises 1738, calculate the derivative. dx x=3 , y = 1 x + 10
 3.3.20: In Exercises 1738, calculate the derivative. dx x=2 , z = x 3x2 + 1
 3.3.21: In Exercises 1738, calculate the derivative. x) = ( x + 1)(x 1)
 3.3.22: In Exercises 1738, calculate the derivative. x) = 9x5/2 2 x
 3.3.23: In Exercises 1738, calculate the derivative. dx x=2 , y = x4 4 x2 5
 3.3.24: In Exercises 1738, calculate the derivative. x) = x4 + ex x + 1
 3.3.25: In Exercises 1738, calculate the derivative. dx x=1 , z = 1 x3 + 1
 3.3.26: In Exercises 1738, calculate the derivative. x) = 3x3 x2 + 2 x
 3.3.27: In Exercises 1738, calculate the derivative. ) = t (t + 1)(t2 + 1)
 3.3.28: In Exercises 1738, calculate the derivative. x) = x3/2 2x4 3x + x1/2
 3.3.29: In Exercises 1738, calculate the derivative. t) = 31/2 51/2
 3.3.30: In Exercises 1738, calculate the derivative. ) = 2(x 1)
 3.3.31: In Exercises 1738, calculate the derivative. x) = (x + 3)(x 1)(x 5)
 3.3.32: In Exercises 1738, calculate the derivative. x) = ex (x2 + 1)(x + 4)
 3.3.33: In Exercises 1738, calculate the derivative. x) = ex x + 1
 3.3.34: In Exercises 1738, calculate the derivative. ) = ex+1 + ex e + 1
 3.3.35: In Exercises 1738, calculate the derivative. ) = z2 4 z 1 z2 1 z + ...
 3.3.36: In Exercises 1738, calculate the derivative. x (ax + b)(abx2 + 1) (...
 3.3.37: In Exercises 1738, calculate the derivative. t xt 4 t2 x (x constant)
 3.3.38: In Exercises 1738, calculate the derivative. x ax + b cx + d (a, b,...
 3.3.39: In Exercises 3942, calculate the derivative using the values: f (4)...
 3.3.40: In Exercises 3942, calculate the derivative using the values: F (4)...
 3.3.41: In Exercises 3942, calculate the derivative using the values: G (4)...
 3.3.42: In Exercises 3942, calculate the derivative using the values: H (4)...
 3.3.43: Calculate F (0), where F (x) = x9 + x8 + 4x5 7x x4 3x2 + 2x + 1 Hin...
 3.3.44: Proceed as in Exercise 43 to calculate F (0), where F (x) = 1 + x +...
 3.3.45: Use the Product Rule to calculate d dx e2x .
 3.3.46: Plot the derivative of f (x) = x/(x2 + 1) over [4, 4]. Use the grap...
 3.3.47: Plot f (x) = x/(x2 1) (in a suitably bounded viewing box). Use the ...
 3.3.48: Let P = V 2R/(R + r)2 as in Example 7. Calculate dP/dr, assuming th...
 3.3.49: Find a > 0 such that the tangent line to the graph of f (x) = x2ex ...
 3.3.50: Current I (amperes), voltage V (volts), and resistance R (ohms) in ...
 3.3.51: Current I (amperes), voltage V (volts), and resistance R (ohms) in ...
 3.3.52: The tip speed ratio of a turbine (Figure 5) is the ratio R = T/W, w...
 3.3.53: The curve y = 1/(x2 + 1) is called the witch of Agnesi (Figure 6) a...
 3.3.54: Let f (x) = g(x) = x. Show that (f/g) = f /g
 3.3.55: Use the Product Rule to show that (f 2) = 2ff . 5
 3.3.56: Show that (f 3) = 3f 2f .
 3.3.57: Let f , g, h be differentiable functions. Show that (fgh) (x) is eq...
 3.3.58: Prove the Quotient Rule using the limit definition of the derivative.
 3.3.59: Derivative of the Reciprocal Use the limit definition to prove d dx...
 3.3.60: Prove the Quotient Rule using Eq. (7) and the Product Rule.
 3.3.61: Use the limit definition of the derivative to prove the following s...
 3.3.62: Carry out Maria Agnesis proof of the Quotient Rule from her book on...
 3.3.63: The Power Rule Revisited If you are familiar with proof by inductio...
 3.3.64: Exercises 64 and 65: A basic fact of algebra states that c is a roo...
 3.3.65: Use Exercise 64 to determine whether c = 1 is a multiple root: (a) ...
 3.3.66: Figure 7 is the graph of a polynomial with roots at A, B, and C. Wh...
 3.3.67: According to Eq. (8) in Section 3.2, d dx bx = m(b) bx. Use t
Solutions for Chapter 3.3: Product and Quotient Rules
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 3.3: Product and Quotient Rules
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Chapter 3.3: Product and Quotient Rules includes 67 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 67 problems in chapter 3.3: Product and Quotient Rules have been answered, more than 44850 students have viewed full stepbystep solutions from this chapter.

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.

Complex conjugates
Complex numbers a + bi and a  bi

Convenience sample
A sample that sacrifices randomness for convenience

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Equivalent vectors
Vectors with the same magnitude and direction.

Event
A subset of a sample space.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Initial value of a function
ƒ 0.

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

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Negative angle
Angle generated by clockwise rotation.

Position vector of the point (a, b)
The vector <a,b>.

Projectile motion
The movement of an object that is subject only to the force of gravity

Statistic
A number that measures a quantitative variable for a sample from a population.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Vertex of a cone
See Right circular cone.

Vertical asymptote
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a ƒ1x2 = q.

yzplane
The points (0, y, z) in Cartesian space.