 3.1: Find the derivatives of the functions in Exercises 1 64.
 3.2: Find the derivatives of the functions in Exercises 1 64.
 3.3: Find the derivatives of the functions in Exercises 1 64.
 3.4: Find the derivatives of the functions in Exercises 1 64.
 3.5: Find the derivatives of the functions in Exercises 1 64.
 3.6: Find the derivatives of the functions in Exercises 1 64.
 3.7: Find the derivatives of the functions in Exercises 1 64.
 3.8: Find the derivatives of the functions in Exercises 1 64.
 3.9: Find the derivatives of the functions in Exercises 1 64.
 3.10: Find the derivatives of the functions in Exercises 1 64.
 3.11: Find the derivatives of the functions in Exercises 1 64.
 3.12: Find the derivatives of the functions in Exercises 1 64.
 3.13: Find the derivatives of the functions in Exercises 1 64.
 3.14: Find the derivatives of the functions in Exercises 1 64.
 3.15: Find the derivatives of the functions in Exercises 1 64.
 3.16: Find the derivatives of the functions in Exercises 1 64.
 3.17: Find the derivatives of the functions in Exercises 1 64.
 3.18: Find the derivatives of the functions in Exercises 1 64.
 3.19: Find the derivatives of the functions in Exercises 1 64.
 3.20: Find the derivatives of the functions in Exercises 1 64.
 3.21: Find the derivatives of the functions in Exercises 1 64.
 3.22: Find the derivatives of the functions in Exercises 1 64.
 3.23: Find the derivatives of the functions in Exercises 1 64.
 3.24: Find the derivatives of the functions in Exercises 1 64.
 3.25: Find the derivatives of the functions in Exercises 1 64.
 3.26: Find the derivatives of the functions in Exercises 1 64.
 3.27: Find the derivatives of the functions in Exercises 1 64.
 3.28: Find the derivatives of the functions in Exercises 1 64.
 3.29: Find the derivatives of the functions in Exercises 1 64.
 3.30: Find the derivatives of the functions in Exercises 1 64.
 3.31: Find the derivatives of the functions in Exercises 1 64.
 3.32: Find the derivatives of the functions in Exercises 1 64.
 3.33: Find the derivatives of the functions in Exercises 1 64.
 3.34: Find the derivatives of the functions in Exercises 1 64.
 3.35: Find the derivatives of the functions in Exercises 1 64.
 3.36: Find the derivatives of the functions in Exercises 1 64.
 3.37: Find the derivatives of the functions in Exercises 1 64.
 3.38: Find the derivatives of the functions in Exercises 1 64.
 3.39: Find the derivatives of the functions in Exercises 1 64.
 3.40: Find the derivatives of the functions in Exercises 1 64.
 3.41: Find the derivatives of the functions in Exercises 1 64.
 3.42: Find the derivatives of the functions in Exercises 1 64.
 3.43: Find the derivatives of the functions in Exercises 1 64.
 3.44: Find the derivatives of the functions in Exercises 1 64.
 3.45: Find the derivatives of the functions in Exercises 1 64.
 3.46: Find the derivatives of the functions in Exercises 1 64.
 3.47: Find the derivatives of the functions in Exercises 1 64.
 3.48: Find the derivatives of the functions in Exercises 1 64.
 3.49: Find the derivatives of the functions in Exercises 1 64.
 3.50: Find the derivatives of the functions in Exercises 1 64.
 3.51: Find the derivatives of the functions in Exercises 1 64.
 3.52: Find the derivatives of the functions in Exercises 1 64.
 3.53: Find the derivatives of the functions in Exercises 1 64.
 3.54: Find the derivatives of the functions in Exercises 1 64.
 3.55: Find the derivatives of the functions in Exercises 1 64.
 3.56: Find the derivatives of the functions in Exercises 1 64.
 3.57: Find the derivatives of the functions in Exercises 1 64.
 3.58: Find the derivatives of the functions in Exercises 1 64.
 3.59: Find the derivatives of the functions in Exercises 1 64.
 3.60: Find the derivatives of the functions in Exercises 1 64.
 3.61: Find the derivatives of the functions in Exercises 1 64.
 3.62: Find the derivatives of the functions in Exercises 1 64.
 3.63: Find the derivatives of the functions in Exercises 1 64.
 3.64: Find the derivatives of the functions in Exercises 1 64.
 3.65: In Exercises 6578, find by implicit differentiation.
 3.66: In Exercises 6578, find by implicit differentiation.
 3.67: In Exercises 6578, find by implicit differentiation.
 3.68: In Exercises 6578, find by implicit differentiation.
 3.69: In Exercises 6578, find by implicit differentiation.
 3.70: In Exercises 6578, find by implicit differentiation.
 3.71: In Exercises 6578, find by implicit differentiation.
 3.72: In Exercises 6578, find by implicit differentiation.
 3.73: In Exercises 6578, find by implicit differentiation.
 3.74: In Exercises 6578, find by implicit differentiation.
 3.75: In Exercises 6578, find by implicit differentiation.
 3.76: In Exercises 6578, find by implicit differentiation.
 3.77: In Exercises 6578, find by implicit differentiation.
 3.78: In Exercises 6578, find by implicit differentiation.
 3.79: In Exercises 79 and 80, find
 3.80: In Exercises 79 and 80, find
 3.81: In Exercises 81 and 82, find
 3.82: In Exercises 81 and 82, find
 3.83: Find by implicit differentiation
 3.84: a. By differentiating implicitly, show that b. Then show that d2 y>...
 3.85: Suppose that functions (x) and g(x) and their first derivatives hav...
 3.86: Suppose that the function (x) and its first derivative have the fol...
 3.87: Find the value of at
 3.88: Find the value of
 3.89: Find the value of
 3.90: Find the value of
 3.91: If find the value of at the point (0, 1)
 3.92: If find at the point (8, 8)
 3.93: In Exercises 93 and 94, find the derivative using the definition.
 3.94: In Exercises 93 and 94, find the derivative using the definition.
 3.95: a. Graph the function b. Is continuous at c. Is differentiable at G...
 3.96: a. Graph the function b. Is continuous at c. Is differentiable at G...
 3.97: a. Graph the function b. Is continuous at c. Is differentiable at
 3.98: For what value or values of the constant m, if any, is a. continuou...
 3.99: Are there any points on the curve where the slope is If so, find them.
 3.100: Are there any points on the curve where the slope is 2? If so, find...
 3.101: Find the points on the curve where the tangent is parallel to the x...
 3.102: Find the x and yintercepts of the line that is tangent to the cur...
 3.103: Find the points on the curve where the tangent is a. perpendicular ...
 3.104: Show that the tangents to the curve at and intersect at right angles.
 3.105: Find the points on the curve where the normal is parallel to the li...
 3.106: Find equations for the tangent and normal to the curve at the point...
 3.107: The parabola is to be tangent to the line Find C
 3.108: Show that the tangent to the curve at any point meets the curve aga...
 3.109: For what value of c is the curve tangent to the line through the po...
 3.110: Show that the normal line at any point of the circle x passes throu...
 3.111: In Exercises 111116, find equations for the lines that are tangent ...
 3.112: In Exercises 111116, find equations for the lines that are tangent ...
 3.113: In Exercises 111116, find equations for the lines that are tangent ...
 3.114: In Exercises 111116, find equations for the lines that are tangent ...
 3.115: In Exercises 111116, find equations for the lines that are tangent ...
 3.116: In Exercises 111116, find equations for the lines that are tangent ...
 3.117: Find the slope of the curve at the points (1, 1) and
 3.118: The graph shown suggests that the curve might have horizontal tange...
 3.119: Each of the figures in Exercises 119 and 120 shows two graphs, the ...
 3.120: Each of the figures in Exercises 119 and 120 shows two graphs, the ...
 3.121: Use the following information to graph the function for i) The grap...
 3.122: Repeat Exercise 121, supposing that the graph starts at instead of ...
 3.123: a. What is the value of the derivative of the rabbit population whe...
 3.124: In what units should the slopes of the rabbit and fox population cu...
 3.125: Find the limits in Exercises 125132
 3.126: Find the limits in Exercises 125133
 3.127: Find the limits in Exercises 125134
 3.128: Find the limits in Exercises 125135
 3.129: Find the limits in Exercises 125136
 3.130: Find the limits in Exercises 125137
 3.131: Find the limits in Exercises 125138
 3.132: Find the limits in Exercises 125139
 3.133: Show how to extend the functions in Exercises 133 and 134 to be con...
 3.134: Show how to extend the functions in Exercises 133 and 134 to be con...
 3.135: In Exercises 135140, use logarithmic differentiation to find the de...
 3.136: In Exercises 135140, use logarithmic differentiation to find the de...
 3.137: In Exercises 135140, use logarithmic differentiation to find the de...
 3.138: In Exercises 135140, use logarithmic differentiation to find the de...
 3.139: In Exercises 135140, use logarithmic differentiation to find the de...
 3.140: In Exercises 135140, use logarithmic differentiation to find the de...
 3.141: Right circular cylinder The total surface area S of a right circula...
 3.142: Right circular cone The lateral surface area S of a right circular ...
 3.143: The radius of a circle is changing at the rate of At what rate is t...
 3.144: The volume of a cube is increasing at the rate of at the instant it...
 3.145: If two resistors of and ohms are connected in parallel in an electr...
 3.146: The impedance Z (ohms) in a series circuit is related to the resist...
 3.147: The coordinates of a particle moving in the metric xyplane are dif...
 3.148: A particle moves along the curve in the first quadrant in such a wa...
 3.149: Water drains from the conical tank shown in the accompanying figure...
 3.150: As television cable is pulled from a large spool to be strung from ...
 3.151: The figure shows a boat 1 km offshore, sweeping the shore with a se...
 3.152: Points A and B move along the x and yaxes, respectively, in such ...
 3.153: Find the linearizations of a. b. Graph the curves and linearization...
 3.154: We can obtain a useful linear approximation of the function by comb...
 3.155: Find the linearization of
 3.156: Find the linearization of
 3.157: Write a formula that estimates the change that occurs in the latera...
 3.158: Controlling error a. How accurately should you measure the edge of ...
 3.159: The circumference of the equator of a sphere is measured as 10 cm w...
 3.160: To find the height of a lamppost (see accompanying figure), you sta...
Solutions for Chapter 3: Differentiation
Full solutions for Thomas' Calculus Early Transcendentals  12th Edition
ISBN: 9780321588760
Solutions for Chapter 3: Differentiation
Get Full SolutionsThis textbook survival guide was created for the textbook: Thomas' Calculus Early Transcendentals, edition: 12. Thomas' Calculus Early Transcendentals was written by and is associated to the ISBN: 9780321588760. Since 160 problems in chapter 3: Differentiation have been answered, more than 8002 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3: Differentiation includes 160 full stepbystep solutions.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Directed distance
See Polar coordinates.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Implied domain
The domain of a function’s algebraic expression.

Initial side of an angle
See Angle.

kth term of a sequence
The kth expression in the sequence

Linear system
A system of linear equations

Obtuse triangle
A triangle in which one angle is greater than 90°.

Pie chart
See Circle graph.

Polar axis
See Polar coordinate system.

Positive linear correlation
See Linear correlation.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

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.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

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

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Variance
The square of the standard deviation.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.