 2.1: In Exercises 14, find the derivative of the function by using the d...
 2.2: In Exercises 14, find the derivative of the function by using the d...
 2.3: In Exercises 14, find the derivative of the function by using the d...
 2.4: In Exercises 14, find the derivative of the function by using the d...
 2.5: In Exercises 5 and 6, describe the values at which is differentiab...
 2.6: In Exercises 5 and 6, describe the values at which is differentiab...
 2.7: Sketch the graph of (a) Is continuous at (b) Is differentiable at E...
 2.8: Sketch the graph of (a) Is continuous at (b) Is differentiable at E...
 2.9: In Exercises 9 and 10, find the slope of the tangent line to the gr...
 2.10: In Exercises 9 and 10, find the slope of the tangent line to the gr...
 2.11: In Exercises 11 and 12, (a) find an equation of the tangent line to...
 2.12: In Exercises 11 and 12, (a) find an equation of the tangent line to...
 2.13: In Exercises 13 and 14, use the alternative form of the derivative ...
 2.14: In Exercises 13 and 14, use the alternative form of the derivative ...
 2.15: In Exercises 1530, find the derivative of the function. xy210xy
 2.16: In Exercises 1530, find the derivative of the function. 210xy
 2.17: In Exercises 1530, find the derivative of the function. 10xy4
 2.18: In Exercises 1530, find the derivative of the function. 10xy4y
 2.19: In Exercises 1530, find the derivative of the function. xy4y
 2.20: In Exercises 1530, find the derivative of the function. 4yx
 2.21: In Exercises 1530, find the derivative of the function. 4yx3
 2.22: In Exercises 1530, find the derivative of the function. yx3
 2.23: In Exercises 1530, find the derivative of the function. x3x
 2.24: In Exercises 1530, find the derivative of the function. x3xy
 2.25: In Exercises 1530, find the derivative of the function. 3xy2
 2.26: In Exercises 1530, find the derivative of the function. xy2
 2.27: In Exercises 1530, find the derivative of the function. xy2x
 2.28: In Exercises 1530, find the derivative of the function. y2x3
 2.29: In Exercises 1530, find the derivative of the function. 2x3
 2.30: In Exercises 1530, find the derivative of the function. x34
 2.31: Writing In Exercises 31 and 32, the figure shows the graphs of a fu...
 2.32: Writing In Exercises 31 and 32, the figure shows the graphs of a fu...
 2.33: Vibrating String When a guitar string is plucked, it vibrates with ...
 2.34: Vertical Motion A ball is dropped from a height of 100 feet. One se...
 2.35: Vertical Motion To estimate the height of a building, a weight is d...
 2.36: Vertical Motion A bomb is dropped from an airplane at an altitude o...
 2.37: Projectile Motion A ball thrown follows a path described by (a) Ske...
 2.38: Projectile Motion The path of a projectile thrown at an angle of wi...
 2.39: Horizontal Motion The position function of a particle moving along ...
 2.40: Modeling Data The speed of a car in miles per hour and the stopping...
 2.41: In Exercises 4154, find the derivative of the function. 2y3
 2.42: In Exercises 4154, find the derivative of the function. 2y3x
 2.43: In Exercises 4154, find the derivative of the function. y3x
 2.44: In Exercises 4154, find the derivative of the function. 3x2
 2.45: In Exercises 4154, find the derivative of the function. 3x2
 2.46: In Exercises 4154, find the derivative of the function. x2y
 2.47: In Exercises 4154, find the derivative of the function. 2y
 2.48: In Exercises 4154, find the derivative of the function. 2y
 2.49: In Exercises 4154, find the derivative of the function. yx
 2.50: In Exercises 4154, find the derivative of the function. yx
 2.51: In Exercises 4154, find the derivative of the function. x3
 2.52: In Exercises 4154, find the derivative of the function. x3y
 2.53: In Exercises 4154, find the derivative of the function. x3y
 2.54: In Exercises 4154, find the derivative of the function. 3y
 2.55: In Exercises 5558, find an equation of the tangent line to the grap...
 2.56: In Exercises 5558, find an equation of the tangent line to the grap...
 2.57: In Exercises 5558, find an equation of the tangent line to the grap...
 2.58: In Exercises 5558, find an equation of the tangent line to the grap...
 2.59: Acceleration The velocity of an object in meters per second is Find...
 2.60: Acceleration An automobiles velocity starting from rest is where is...
 2.61: In Exercises 6164, find the second derivative of the function. xy
 2.62: In Exercises 6164, find the second derivative of the function. xyx
 2.63: In Exercises 6164, find the second derivative of the function. yx2
 2.64: In Exercises 6164, find the second derivative of the function. yx2x
 2.65: In Exercises 65 and 66, show that the function satisfies the equati...
 2.66: In Exercises 65 and 66, show that the function satisfies the equati...
 2.67: In Exercises 6778, find the derivative of the function. 2x21
 2.68: In Exercises 6778, find the derivative of the function. x21y
 2.69: In Exercises 6778, find the derivative of the function. 21y
 2.70: In Exercises 6778, find the derivative of the function. 1yx
 2.71: In Exercises 6778, find the derivative of the function. 1yxx
 2.72: In Exercises 6778, find the derivative of the function. yxx2
 2.73: In Exercises 6778, find the derivative of the function. xx2
 2.74: In Exercises 6778, find the derivative of the function. xx21
 2.75: In Exercises 6778, find the derivative of the function. x21xy
 2.76: In Exercises 6778, find the derivative of the function. 21xy
 2.77: In Exercises 6778, find the derivative of the function. 1xy
 2.78: In Exercises 6778, find the derivative of the function. 1xy4
 2.79: In Exercises 7982, find the derivative of the function at the given...
 2.80: In Exercises 7982, find the derivative of the function at the given...
 2.81: In Exercises 7982, find the derivative of the function at the given...
 2.82: In Exercises 7982, find the derivative of the function at the given...
 2.83: In Exercises 8386, use a computer algebra system to find the deriva...
 2.84: In Exercises 8386, use a computer algebra system to find the deriva...
 2.85: In Exercises 8386, use a computer algebra system to find the deriva...
 2.86: In Exercises 8386, use a computer algebra system to find the deriva...
 2.87: In Exercises 8790, (a) use a computer algebra system to find the de...
 2.88: In Exercises 8790, (a) use a computer algebra system to find the de...
 2.89: In Exercises 8790, (a) use a computer algebra system to find the de...
 2.90: In Exercises 8790, (a) use a computer algebra system to find the de...
 2.91: In Exercises 9194, find the second derivative of the function. x3
 2.92: In Exercises 9194, find the second derivative of the function. x3xy
 2.93: In Exercises 9194, find the second derivative of the function. x3xy2
 2.94: In Exercises 9194, find the second derivative of the function. 3xy2
 2.95: In Exercises 95 98, use a computer algebra system to find the secon...
 2.96: In Exercises 95 98, use a computer algebra system to find the secon...
 2.97: In Exercises 95 98, use a computer algebra system to find the secon...
 2.98: In Exercises 95 98, use a computer algebra system to find the secon...
 2.99: Refrigeration The temperature of food put in a freezer is where is ...
 2.100: Fluid Flow The emergent velocity of a liquid flowing from a hole in...
 2.101: In Exercises 101106, use implicit differentiation to find 4yx
 2.102: In Exercises 101106, use implicit differentiation to find 4yx3
 2.103: In Exercises 101106, use implicit differentiation to find yx3
 2.104: In Exercises 101106, use implicit differentiation to find x3x
 2.105: In Exercises 101106, use implicit differentiation to find x3xy
 2.106: In Exercises 101106, use implicit differentiation to find 3xy2
 2.107: In Exercises 107 and 108, find the equations of the tangent line an...
 2.108: In Exercises 107 and 108, find the equations of the tangent line an...
 2.109: A point moves along the curve in such a way that the value is incre...
 2.110: Surface Area The edges of a cube are expanding at a rate of 5 centi...
 2.111: Depth The cross section of a fivemeter trough is an isosceles trap...
 2.112: Linear and Angular Velocity A rotating beacon is located 1 kilomete...
 2.113: Moving Shadow A sandbag is dropped from a balloon at a height of 60...
 2.1: Consider the graph of the parabola (a) Find the radius of the large...
 2.2: Graph the two parabolas and in the same coordinate plane. Find equa...
 2.3: (a) Find the polynomial whose value and slope agree with the value ...
 2.4: (a) Find an equation of the tangent line to the parabola at the poi...
 2.5: Find a thirddegree polynomial that is tangent to the line at the p...
 2.6: Find a function of the form that is tangent to the line at the poin...
 2.7: The graph of the eight curve, is shown below. (a) Explain how you c...
 2.8: The graph of the pearshaped quartic, is shown below. (a) Explain h...
 2.9: A man 6 feet tall walks at a rate of 5 feet per second toward a str...
 2.10: A particle is moving along the graph of (see figure). When the comp...
 2.11: Let be a differentiable function for all Prove that if for all and ...
 2.12: Let be a function satisfying Prove that if for all and then is diff...
 2.13: The fundamental limit assumes that is measured in radians. What hap...
 2.14: An astronaut standing on the moon throws a rock into the air. The h...
 2.15: If is the acceleration of an object, the jerk is defined by (a) Use...
Solutions for Chapter 2: Differentiation
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 2: Differentiation
Get Full SolutionsChapter 2: Differentiation includes 128 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 128 problems in chapter 2: Differentiation have been answered, more than 76547 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981.

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Division
a b = aa 1 b b, b Z 0

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Exponential regression
A procedure for fitting an exponential function to a set of data.

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

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)

Measure of spread
A measure that tells how widely distributed data are.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Objective function
See Linear programming problem.

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Relevant domain
The portion of the domain applicable to the situation being modeled.

Sample space
Set of all possible outcomes of an experiment.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data