 3.2.1: In Exercises 1 and 2, use the graph to estimate the slope of the ta...
 3.2.2: In Exercises 1 and 2, use the graph to estimate the slope of the ta...
 3.2.3: In Exercises 3 24, find the derivative of the function.y 8 f
 3.2.4: In Exercises 3 24, find the derivative of the function.fx 6x
 3.2.5: In Exercises 3 24, find the derivative of the function.
 3.2.6: In Exercises 3 24, find the derivative of the function.y 1x8 y
 3.2.7: In Exercises 3 24, find the derivative of the function.
 3.2.8: In Exercises 3 24, find the derivative of the function.
 3.2.9: In Exercises 3 24, find the derivative of the function.fx x 1 gx
 3.2.10: In Exercises 3 24, find the derivative of the function.
 3.2.11: In Exercises 3 24, find the derivative of the function.y t ft 2t 2 ...
 3.2.12: In Exercises 3 24, find the derivative of the function.y t ft 2t 2 ...
 3.2.13: In Exercises 3 24, find the derivative of the function.gx x 2 4x3y
 3.2.14: In Exercises 3 24, find the derivative of the function.y 8 x3 g
 3.2.15: In Exercises 3 24, find the derivative of the function.
 3.2.16: In Exercises 3 24, find the derivative of the function.
 3.2.17: In Exercises 3 24, find the derivative of the function.fx 6x 5exf
 3.2.18: In Exercises 3 24, find the derivative of the function.ht t 3 2et f
 3.2.19: In Exercises 3 24, find the derivative of the function.
 3.2.20: In Exercises 3 24, find the derivative of the function.gt cos t2
 3.2.21: In Exercises 3 24, find the derivative of the function.
 3.2.22: In Exercises 3 24, find the derivative of the function.y 5 sin x 2
 3.2.23: In Exercises 3 24, find the derivative of the function.
 3.2.24: In Exercises 3 24, find the derivative of the function.y 34e y x 2 ...
 3.2.25: In Exercises 2530, complete the table using Example 6 as a model.y ...
 3.2.26: In Exercises 2530, complete the table using Example 6 as a model.y ...
 3.2.27: In Exercises 2530, complete the table using Example 6 as a model.y ...
 3.2.28: In Exercises 2530, complete the table using Example 6 as a model.y ...
 3.2.29: In Exercises 2530, complete the table using Example 6 as a model.y xx
 3.2.30: In Exercises 2530, complete the table using Example 6 as a model.y 4x3
 3.2.31: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.32: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.33: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.34: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.35: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.36: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.37: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.38: In Exercises 3138, find the slope of the graph of the function at t...
 3.2.39: In Exercises 3952, find the derivative of the function.gt t 2 4t3g
 3.2.40: In Exercises 3952, find the derivative of the function.
 3.2.41: In Exercises 3952, find the derivative of the function.fx x3 3x2 4x2f
 3.2.42: In Exercises 3952, find the derivative of the function.
 3.2.43: In Exercises 3952, find the derivative of the function.
 3.2.44: In Exercises 3952, find the derivative of the function.y 3x6x 5x2 y
 3.2.45: In Exercises 3952, find the derivative of the function.fx x 6 x 3 xy
 3.2.46: In Exercises 3952, find the derivative of the function.fx 3 x 5x
 3.2.47: In Exercises 3952, find the derivative of the function.
 3.2.48: In Exercises 3952, find the derivative of the function.
 3.2.49: In Exercises 3952, find the derivative of the function.fx 6x 5 cos x
 3.2.50: In Exercises 3952, find the derivative of the function.
 3.2.51: In Exercises 3952, find the derivative of the function.fx x2 2ex
 3.2.52: In Exercises 3952, find the derivative of the function.gx x 3ex f
 3.2.53: In Exercises 5356, (a) find an equation of the tangent line to the ...
 3.2.54: In Exercises 5356, (a) find an equation of the tangent line to the ...
 3.2.55: In Exercises 5356, (a) find an equation of the tangent line to the ...
 3.2.56: In Exercises 5356, (a) find an equation of the tangent line to the ...
 3.2.57: In Exercises 5762, determine the point(s) (if any) at which the gra...
 3.2.58: In Exercises 5762, determine the point(s) (if any) at which the gra...
 3.2.59: In Exercises 5762, determine the point(s) (if any) at which the gra...
 3.2.60: In Exercises 5762, determine the point(s) (if any) at which the gra...
 3.2.61: In Exercises 5762, determine the point(s) (if any) at which the gra...
 3.2.62: In Exercises 5762, determine the point(s) (if any) at which the gra...
 3.2.63: In Exercises 6366, find such that the line is tangent to the graph ...
 3.2.64: In Exercises 6366, find such that the line is tangent to the graph ...
 3.2.65: In Exercises 6366, find such that the line is tangent to the graph ...
 3.2.66: In Exercises 6366, find such that the line is tangent to the graph ...
 3.2.67: Use the graph of to answer each question. To print an enlarged copy...
 3.2.68: Sketch the graph of a function such that for all and the rate of ch...
 3.2.69: In Exercises 69 and 70, the relationship between and is given. Expl...
 3.2.70: In Exercises 69 and 70, the relationship between and is given. Expl...
 3.2.71: In Exercises 71 and 72, the graphs of a function and its derivative...
 3.2.72: In Exercises 71 and 72, the graphs of a function and its derivative...
 3.2.73: Sketch the graphs of and and sketch the two lines that are tangent ...
 3.2.74: Show that the graphs of the two equations and have tangent lines th...
 3.2.75: Show that the graph of the function does not have a horizontal tang...
 3.2.76: Show that the graph of the function does not have a tangent line wi...
 3.2.77: In Exercises 77 and 78, find an equation of the tangent line to the...
 3.2.78: In Exercises 77 and 78, find an equation of the tangent line to the...
 3.2.79: Linear Approximation Use a graphing utility (in square mode) to zoo...
 3.2.80: Linear Approximation Use a graphing utility (in square mode) to zoo...
 3.2.81: Linear Approximation Consider the function with the solution point ...
 3.2.82: Linear Approximation Repeat Exercise 81 for the function where is t...
 3.2.83: True or False? In Exercises 8388, determine whether the statement i...
 3.2.84: True or False? In Exercises 8388, determine whether the statement i...
 3.2.85: True or False? In Exercises 8388, determine whether the statement i...
 3.2.86: True or False? In Exercises 8388, determine whether the statement i...
 3.2.87: True or False? In Exercises 8388, determine whether the statement i...
 3.2.88: True or False? In Exercises 8388, determine whether the statement i...
 3.2.89: In Exercises 8992, find the average rate of change of the function ...
 3.2.90: In Exercises 8992, find the average rate of change of the function ...
 3.2.91: In Exercises 8992, find the average rate of change of the function ...
 3.2.92: In Exercises 8992, find the average rate of change of the function ...
 3.2.93: Vertical Motion In Exercises 93 and 94, use the position function f...
 3.2.94: Vertical Motion In Exercises 93 and 94, use the position function f...
 3.2.95: Vertical Motion In Exercises 95 and 96, use the position function f...
 3.2.96: Vertical Motion In Exercises 95 and 96, use the position function f...
 3.2.97: hink About It In Exercises 97 and 98, the graph of a position funct...
 3.2.98: Think About It In Exercises 97 and 98, the graph of a position func...
 3.2.99: Think About It In Exercises 97 and 98, the graph of a position func...
 3.2.100: Think About It In Exercises 97 and 98, the graph of a position func...
 3.2.101: Modeling Data The stopping distance of an automobile, on dry, level...
 3.2.102: Fuel Cost A car is driven 15,000 miles a year and gets miles per ga...
 3.2.103: Volume The volume of a cube with sides of length is given by Find t...
 3.2.104: Area The area of a square with sides of length is given by Find the...
 3.2.105: Velocity Verify that the average velocity over the time interval is...
 3.2.106: Inventory Management The annual inventory cost for a manufacturer i...
 3.2.107: Writing The number of gallons of regular unleaded gasoline sold by ...
 3.2.108: Newtons Law of Cooling This law states that the rate of change of t...
 3.2.109: Find an equation of the parabola that passes through and is tangent...
 3.2.110: Let be an arbitrary point on the graph of Prove that the area of th...
 3.2.111: Find the tangent line(s) to the curve through the point
 3.2.112: Find the equation(s) of the tangent line(s) to the parabola through...
 3.2.113: In Exercises 113 and 114, find and such that is differentiable ever...
 3.2.114: In Exercises 113 and 114, find and such that is differentiable ever...
 3.2.115: Where are the functions and differentiable?
 3.2.116: Prove that ddx cos x sin x.
Solutions for Chapter 3.2: Basic Differentiation Rules and Rates of Change
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 3.2: Basic Differentiation Rules and Rates of Change
Get Full SolutionsSince 116 problems in chapter 3.2: Basic Differentiation Rules and Rates of Change have been answered, more than 44433 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. Chapter 3.2: Basic Differentiation Rules and Rates of Change includes 116 full stepbystep solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245.

Acute angle
An angle whose measure is between 0° and 90°

Acute triangle
A triangle in which all angles measure less than 90°

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Convenience sample
A sample that sacrifices randomness for convenience

Descriptive statistics
The gathering and processing of numerical information

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Frequency table (in statistics)
A table showing frequencies.

Inverse cotangent function
The function y = cot1 x

Limit to growth
See Logistic growth function.

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Nappe
See Right circular cone.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Proportional
See Power function

Range (in statistics)
The difference between the greatest and least values in a data set.

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

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Unit ratio
See Conversion factor.

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

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.

xyplane
The points x, y, 0 in Cartesian space.