- 3.1: ?Finding the Derivative by the Limit Process In Exercises 1–4, find...
- 3.2: ?Finding the Derivative by the Limit Process In Exercises 1–4, find...
- 3.3: ?Finding the Derivative by the Limit Process In Exercises 1–4, find...
- 3.4: ?Finding the Derivative by the Limit Process In Exercises 1–4, find...
- 3.5: ?Using the Alternative Form of the Derivative In Exercises 5 and 6,...
- 3.6: ?Using the Alternative Form of the Derivative In Exercises 5 and 6,...
- 3.7: ?Determining Differentiability In Exercises 7 and 8, describe the x...
- 3.8: ?Determining Differentiability In Exercises 7 and 8, describe the x...
- 3.9: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.10: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.11: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.12: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.13: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.14: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.15: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.16: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.17: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.18: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.19: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.20: ?Finding a Derivative In Exercises 9–20, use the rules of different...
- 3.21: ?Finding the Slope of a Graph In Exercises 21–24, find the slope of...
- 3.22: ?Finding the Slope of a Graph In Exercises 21–24, find the slope of...
- 3.23: ?Finding the Slope of a Graph In Exercises 21–24, find the slope of...
- 3.24: ?Finding the Slope of a Graph In Exercises 21–24, find the slope of...
- 3.25: ?Vibrating String When a guitar string is plucked, it vibrates with...
- 3.26: ?Volume The surface area of a cube with sides of length s is given ...
- 3.27: ?Vertical Motion In Exercises 27 and 28, use the position function ...
- 3.28: To estimate the height of a building, a weight is dropped from the ...
- 3.29: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.30: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.31: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.32: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.33: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.34: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.35: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.36: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.37: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.38: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.39: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.40: ?Finding a Derivative In Exercises 29– 40, find the derivative of t...
- 3.41: ?Finding an Equation of a Tangent Line In Exercises 41–44, find an ...
- 3.42: ?Finding an Equation of a Tangent Line In Exercises 41–44, find an ...
- 3.43: ?Finding an Equation of a Tangent Line In Exercises 41–44, find an ...
- 3.44: ?Finding an Equation of a Tangent Line In Exercises 41–44, find an ...
- 3.45: ?Finding a Second Derivative In Exercises 45–50, find the second de...
- 3.46: ?Finding a Second Derivative In Exercises 45–50, find the second de...
- 3.47: ?Finding a Second Derivative In Exercises 45–50, find the second de...
- 3.48: ?Finding a Second Derivative In Exercises 45–50, find the second de...
- 3.49: ?Finding a Second Derivative In Exercises 45–50, find the second de...
- 3.50: ?Finding a Second Derivative In Exercises 45–50, find the second de...
- 3.51: ?Acceleration The velocity of an object in meters per second is \(v...
- 3.52: ?Acceleration The velocity of an automobile starting from rest is \...
- 3.53: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.54: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.55: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.56: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.57: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.58: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.59: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.60: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.61: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.62: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.63: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.64: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.65: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.66: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.67: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.68: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.69: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.70: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.71: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.72: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.73: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.74: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.75: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.76: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.77: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.78: ?Finding a Derivative In Exercises 53–78, find the derivative of th...
- 3.79: ?Evaluating a Derivative In Exercises 79–84, find and evaluate the ...
- 3.80: ?Evaluating a Derivative In Exercises 79–84, find and evaluate the ...
- 3.81: ?Evaluating a Derivative In Exercises 79–84, find and evaluate the ...
- 3.82: ?Evaluating a Derivative In Exercises 79–84, find and evaluate the ...
- 3.83: ?Evaluating a Derivative In Exercises 79–84, find and evaluate the ...
- 3.84: ?Evaluating a Derivative In Exercises 79–84, find and evaluate the ...
- 3.85: ?Finding a Second Derivative In Exercises 85–88, find the second de...
- 3.86: ?Finding a Second Derivative In Exercises 85–88, find the second de...
- 3.87: ?Finding a Second Derivative In Exercises 85–88, find the second de...
- 3.88: ?Finding a Second Derivative In Exercises 85–88, find the second de...
- 3.89: ?Refrigeration The temperature T (in degrees Fahrenheit) of food in...
- 3.90: ?Harmonic Motion The displacement from equilibrium of an object in ...
- 3.91: ?Modeling Data The atmospheric pressure decreases with increasing a...
- 3.92: ?Tractrix A person walking along a dock drags a boat by a 10-meter ...
- 3.93: ?Finding a Derivative In Exercises 93–98, find \(d y / d x\) implic...
- 3.94: ?Finding a Derivative In Exercises 93–98, find \(d y / d x\) implic...
- 3.95: ?Finding a Derivative In Exercises 93–98, find \(d y / d x\) implic...
- 3.96: ?Finding a Derivative In Exercises 93–98, find \(d y / d x\) implic...
- 3.97: ?Finding a Derivative In Exercises 93–98, find \(d y / d x\) implic...
- 3.98: ?Finding a Derivative In Exercises 93–98, find \(d y / d x\) implic...
- 3.99: ?Tangent Lines and Normal Lines In Exercises 99–102, find equations...
- 3.100: ?Tangent Lines and Normal Lines In Exercises 99–102, find equations...
- 3.101: ?Tangent Lines and Normal Lines In Exercises 99–102, find equations...
- 3.102: ?Tangent Lines and Normal Lines In Exercises 99–102, find equations...
- 3.103: ?Logarithmic Differentiation In Exercises 103 and 104, use logarith...
- 3.104: ?Logarithmic Differentiation In Exercises 103 and 104, use logarith...
- 3.105: ?Evaluating the Derivative of an Inverse Function In Exercises 105–...
- 3.106: ?Evaluating the Derivative of an Inverse Function In Exercises 105–...
- 3.107: ?Evaluating the Derivative of an Inverse Function In Exercises 105–...
- 3.108: ?Evaluating the Derivative of an Inverse Function In Exercises 105–...
- 3.109: ?Finding a Derivative In Exercises 109–114, find the derivative of ...
- 3.110: ?Finding a Derivative In Exercises 109–114, find the derivative of ...
- 3.111: ?Finding a Derivative In Exercises 109–114, find the derivative of ...
- 3.112: ?Finding a Derivative In Exercises 109–114, find the derivative of ...
- 3.113: ?Finding a Derivative In Exercises 109–114, find the derivative of ...
- 3.114: ?Finding a Derivative In Exercises 109–114, find the derivative of ...
- 3.115: ?Rate of Change A point moves along the curve \(y=\sqrt{x}\) in suc...
- 3.116: All edges of a cube are expanding at a rate of 8 centimeters per se...
- 3.117: ?Linear vs. Angular Speed A rotating beacon is located 1 kilometer ...
- 3.118: ?Moving Shadow A sandbag is dropped from a balloon at a height of 6...
- 3.119: ?Using Newton’s Method In Exercises 119–124, use Newton’s Method to...
- 3.120: ?Using Newton’s Method In Exercises 119–124, use Newton’s Method to...
- 3.121: ?Using Newton’s Method In Exercises 119–124, use Newton’s Method to...
- 3.122: ?Using Newton’s Method In Exercises 119–124, use Newton’s Method to...
- 3.123: ?Using Newton’s Method In Exercises 119–124, use Newton’s Method to...
- 3.124: ?Using Newton’s Method In Exercises 119–124, use Newton’s Method to...
- 3.125: ?Finding Point(s) of Intersection In Exercises 125–128, use Newton’...
- 3.126: ?Finding Point(s) of Intersection In Exercises 125–128, use Newton’...
- 3.127: ?Finding Point(s) of Intersection In Exercises 125–128, use Newton’...
- 3.128: ?Finding Point(s) of Intersection In Exercises 125–128, use Newton’...
Solutions for Chapter 3: Differentiation
Full solutions for Calculus: Early Transcendental Functions | 6th Edition
ISBN: 9781285774770
This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. Since 128 problems in chapter 3: Differentiation have been answered, more than 167813 students have viewed full step-by-step solutions from this chapter. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. Chapter 3: Differentiation includes 128 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.
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Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)
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Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
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Dependent variable
Variable representing the range value of a function (usually y)
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Distance (on a number line)
The distance between real numbers a and b, or |a - b|
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Division
a b = aa 1 b b, b Z 0
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Frequency
Reciprocal of the period of a sinusoid.
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Independent events
Events A and B such that P(A and B) = P(A)P(B)
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Measure of an angle
The number of degrees or radians in an angle
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NDER ƒ(a)
See Numerical derivative of ƒ at x = a.
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Orthogonal vectors
Two vectors u and v with u x v = 0.
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Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
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Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,
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Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.
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Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.
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Reciprocal of a real number
See Multiplicative inverse of a real number.
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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
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Supply curve
p = ƒ(x), where x represents production and p represents price
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Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.
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Weights
See Weighted mean.
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Ymin
The y-value of the bottom of the viewing window.