- 3.1: Firtd dy / dx in 1 through 35
- 3.2: Firtd dy / dx in 1 through 36
- 3.3: Firtd dy / dx in 1 through 37
- 3.4: Firtd dy / dx in 1 through 38
- 3.5: Firtd dy / dx in 1 through 39
- 3.6: Firtd dy / dx in 1 through 40
- 3.7: Firtd dy / dx in 1 through 41
- 3.8: Firtd dy / dx in 1 through 42
- 3.9: Firtd dy / dx in 1 through 43
- 3.10: Firtd dy / dx in 1 through 44
- 3.11: Firtd dy / dx in 1 through 45
- 3.12: Firtd dy / dx in 1 through 46
- 3.13: Firtd dy / dx in 1 through 47
- 3.14: Firtd dy / dx in 1 through 48
- 3.15: Firtd dy / dx in 1 through 49
- 3.16: Firtd dy / dx in 1 through 50
- 3.17: Firtd dy / dx in 1 through 51
- 3.18: Firtd dy / dx in 1 through 52
- 3.19: Firtd dy / dx in 1 through 53
- 3.20: Firtd dy / dx in 1 through 54
- 3.21: Firtd dy / dx in 1 through 55
- 3.22: Firtd dy / dx in 1 through 56
- 3.23: Firtd dy / dx in 1 through 57
- 3.24: Firtd dy / dx in 1 through 58
- 3.25: Firtd dy / dx in 1 through 59
- 3.26: Firtd dy / dx in 1 through 60
- 3.27: Firtd dy / dx in 1 through 61
- 3.28: Firtd dy / dx in 1 through 62
- 3.29: Firtd dy / dx in 1 through 63
- 3.30: Firtd dy / dx in 1 through 64
- 3.31: Firtd dy / dx in 1 through 65
- 3.32: Firtd dy / dx in 1 through 66
- 3.33: Firtd dy / dx in 1 through 67
- 3.34: Firtd dy / dx in 1 through 68
- 3.35: Firtd dy / dx in 1 through 69
- 3.36: Find the derivatives of the functions defined in 36 through 45.
- 3.37: Find the derivatives of the functions defined in 36 through 45.
- 3.38: Find the derivatives of the functions defined in 36 through 45.
- 3.39: Find the derivatives of the functions defined in 36 through 45.
- 3.40: Find the derivatives of the functions defined in 36 through 45.
- 3.41: Find the derivatives of the functions defined in 36 through 45.
- 3.42: Find the derivatives of the functions defined in 36 through 45.
- 3.43: Find the derivatives of the functions defined in 36 through 45.
- 3.44: Find the derivatives of the functions defined in 36 through 45.
- 3.45: Find the derivatives of the functions defined in 36 through 45.
- 3.46: In 46 through 51. fnd dy/dx by implicit differentiation
- 3.47: In 46 through 51. fnd dy/dx by implicit differentiation
- 3.48: In 46 through 51. fnd dy/dx by implicit differentiation
- 3.49: In 46 through 51. fnd dy/dx by implicit differentiation
- 3.50: In 46 through 51. fnd dy/dx by implicit differentiation
- 3.51: In 46 through 51. fnd dy/dx by implicit differentiation
- 3.52: In 52 through 57. fnd dy/dx by logarithmic differentiation
- 3.53: In 52 through 57. fnd dy/dx by logarithmic differentiation
- 3.54: In 52 through 57. fnd dy/dx by logarithmic differentiation
- 3.55: In 52 through 57. fnd dy/dx by logarithmic differentiation
- 3.56: In 52 through 57. fnd dy/dx by logarithmic differentiation
- 3.57: In 52 through 57. fnd dy/dx by logarithmic differentiation
- 3.58: In 58 through 61, write an equation of the line tangent to the give...
- 3.59: In 58 through 61, write an equation of the line tangent to the give...
- 3.60: In 58 through 61, write an equation of the line tangent to the give...
- 3.61: In 58 through 61, write an equation of the line tangent to the give...
- 3.62: If a hemispherical bowl with radius I ft is filled with warer to a ...
- 3.63: Falling sand forms a conical sandpile. Its height,h always remains ...
- 3.64: Find the limits in 64 through 69.
- 3.65: Find the limits in 64 through 69.
- 3.66: Find the limits in 64 through 69.
- 3.67: Find the limits in 64 through 69.
- 3.68: Find the limits in 64 through 69.
- 3.69: Find the limits in 64 through 69.
- 3.70: In 70 through 75, identify the two functions f and g such that h(x)...
- 3.71: In 70 through 75, identify the two functions f and g such that h(x)...
- 3.72: In 70 through 75, identify the two functions f and g such that h(x)...
- 3.73: In 70 through 75, identify the two functions f and g such that h(x)...
- 3.74: In 70 through 75, identify the two functions f and g such that h(x)...
- 3.75: In 70 through 75, identify the two functions f and g such that h(x)...
- 3.76: The period ? ofoscillation (in seconds) ofa simple pendulum of leng...
- 3.77: What is the rate of change of the volume V : jrrrr of a sphere with...
- 3.78: What is an equation for the straight line through ( l. 0) thar is t...
- 3.79: A rocket is launched vertically upward from a point 3 mi west of an...
- 3.80: An oil field containing 20 wells has been producing 4000 banels of ...
- 3.81: A tdangle is inscribed in a circle of radius R. One side of the tri...
- 3.82: A tdangle is inscribed in a circle of radius R. One side of the tri...
- 3.83: A mass of clay of volume V is formed into two spheres. For what dis...
- 3.84: A right triangle has legs of lengths 3 m and 4 m. Whar is the maxim...
- 3.85: What is the maximum possible volun]e of a right circular cone inscr...
- 3.86: A farmer has 400 ft of f'encing with which to build a rect angular ...
- 3.87: In one simple model of the spread of a contagious disease among mem...
- 3.88: Three sidcs of a trapezoid have length L, a constant. What should b...
- 3.89: A box with no top must have a base twice as long as it is wide. and...
- 3.90: A small right circular cone is inscribed in a larger one (Fig. 3.MP...
- 3.91: Two vertices of a trapezoid are at ( -2. 0) and (2. 0). and the oth...
- 3.92: Suppose that I is a ditl'erentiable function defined on the whole r...
- 3.93: Use the result of to show that the minimum dis tance from the point...
- 3.94: A race track is to be built in the shape of two parallel and equal ...
- 3.95: Two towns are located near the straight shore of a lake. Their near...
- 3.96: A hiker finds herself in a lbrest 2 km from a long straight road. S...
- 3.97: When an arrow is shot lioln the origin wirh initial veloc ity i,- a...
- 3.98: A projectile is tired with initial \elocity L'and angle of elevatio...
- 3.99: In 99 through 110, use? Newton's method to find the solution of the...
- 3.100: In 99 through 110, use? Newton's method to find the solution of the...
- 3.101: In 99 through 110, use? Newton's method to find the solution of the...
- 3.102: In 99 through 110, use? Newton's method to find the solution of the...
- 3.103: In 99 through 110, use? Newton's method to find the solution of the...
- 3.104: In 99 through 110, use? Newton's method to find the solution of the...
- 3.105: In 99 through 110, use? Newton's method to find the solution of the...
- 3.106: In 99 through 110, use? Newton's method to find the solution of the...
- 3.107: In 99 through 110, use? Newton's method to find the solution of the...
- 3.108: In 99 through 110, use? Newton's method to find the solution of the...
- 3.109: In 99 through 110, use? Newton's method to find the solution of the...
- 3.110: In 99 through 110, use? Newton's method to find the solution of the...
- 3.111: Find the depth to which a wooden ball with radius 2 ft sinks in wat...
- 3.112: The equation,r': + I : 0 has no real solutions. Try linding a solut...
- 3.113: At the beginning of Section 3.10 we mentioned the lifthdegree equat...
- 3.114: The equation tnn.t:1 has a sequence dl. dr. ai. ... of positive rco...
- 3.115: Criticize the fbllowing "proof'that 3 = 2. Begin by writirlg .rr:.....
- 3.116: show that -:1 '_".t1 1 1),.rr: -- Iim' -' -i.,'t. ;.r2 [Srrggestioa...
- 3.117: Prove that _t r _,.1 .1 D,.t: ' : lim :-r-J [Saggestiol: Factor the...
- 3.118: A rectangulal block with square base is being squeezed in such a wa...
- 3.119: Air is being pumped into a spherical balloon at the constant rate o...
- 3.120: A ladder 10 ft long is leaning against a wall. If the botrom of the...
- 3.121: A water tank in the shape of an inverted cone. axis vertical and ve...
- 3.122: Plane A is flying west toward an airport at an altitude of 2 mi. Pl...
- 3.123: A water tank is shaped in such a way that the volume of water in th...
- 3.124: Water is being poued into the conical tank of at the mte of 50 ft3l...
- 3.125: Let L be a sfiaight line passing through the fixed point P(.r6,1,p)...
Solutions for Chapter 3: The Derivative
Full solutions for Calculus:Early Transcendentals | 7th Edition
ISBN: 9780131569898
Summary of Chapter 3: The Derivative
The definition of the derivative. The rate of change of a function with respect to a variable. Operator notation for derivatives.
This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3: The Derivative includes 125 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Since 125 problems in chapter 3: The Derivative have been answered, more than 40233 students have viewed full step-by-step solutions from this chapter.
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Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
-
Back-to-back stemplot
A stemplot with leaves on either side used to compare two distributions.
-
Base
See Exponential function, Logarithmic function, nth power of a.
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Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists
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Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .
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Focus, foci
See Ellipse, Hyperbola, Parabola.
-
Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.
-
Imaginary part of a complex number
See Complex number.
-
Inverse composition rule
The composition of a one-toone function with its inverse results in the identity function.
-
Jump discontinuity at x a
limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal
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Length of a vector
See Magnitude of a vector.
-
Mean (of a set of data)
The sum of all the data divided by the total number of items
-
Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line
-
Phase shift
See Sinusoid.
-
Polynomial in x
An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)
-
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.
-
Scatter plot
A plot of all the ordered pairs of a two-variable data set on a coordinate plane.
-
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.
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Unbounded interval
An interval that extends to -? or ? (or both).
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Zero factor property
If ab = 0 , then either a = 0 or b = 0.