 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 differentiable.
 2.6: In Exercises 5 and 6, describe the values at which is differentiable.
 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, use the rules of differentiation to find thederi...
 2.16: In Exercises 1530, use the rules of differentiation to find thederi...
 2.17: In Exercises 1530, use the rules of differentiation to find thederi...
 2.18: In Exercises 1530, use the rules of differentiation to find thederi...
 2.19: In Exercises 1530, use the rules of differentiation to find thederi...
 2.20: In Exercises 1530, use the rules of differentiation to find thederi...
 2.21: In Exercises 1530, use the rules of differentiation to find thederi...
 2.22: In Exercises 1530, use the rules of differentiation to find thederi...
 2.23: In Exercises 1530, use the rules of differentiation to find thederi...
 2.24: In Exercises 1530, use the rules of differentiation to find thederi...
 2.25: In Exercises 1530, use the rules of differentiation to find thederi...
 2.26: In Exercises 1530, use the rules of differentiation to find thederi...
 2.27: In Exercises 1530, use the rules of differentiation to find thederi...
 2.28: In Exercises 1530, use the rules of differentiation to find thederi...
 2.29: In Exercises 1530, use the rules of differentiation to find the der...
 2.30: In Exercises 1530, use the rules of differentiation to find the der...
 2.31: In Exercises 31 and 32, the figure shows the graphs of a function a...
 2.32: In Exercises 31 and 32, the figure shows the graphs of a function a...
 2.33: When a guitar string is plucked, it vibrates with a frequency of wh...
 2.34: A ball is dropped from a height of 100 feet. One second later, anot...
 2.35: To estimate the height of a building, a weight is dropped from the ...
 2.36: A bomb is dropped from an airplane at an altitude of 14,400 feet. H...
 2.37: A thrown ball follows a path described by (a) Sketch a graph of the...
 2.38: The path of a projectile thrown at an angle of with level ground is...
 2.39: The position function of a particle moving along the axis is for (a...
 2.40: The speed of a car in miles per hour and the stopping distance in f...
 2.41: In Exercises 4154, find the derivative of the function.fx 5x 2 8x 2...
 2.42: In Exercises 4154, find the derivative of the function.gx x3 7xx 3
 2.43: In Exercises 4154, find the derivative of the function.hx x sin x c
 2.44: In Exercises 4154, find the derivative of the function.
 2.45: In Exercises 4154, find the derivative of the function.fx x 2 x 1 x...
 2.46: In Exercises 4154, find the derivative of the function.fx 6x 5 x 2 1 f
 2.47: In Exercises 4154, find the derivative of the function.fx 1 9 4x 2 f
 2.48: In Exercises 4154, find the derivative of the function.fx 9 3x 2 2x f
 2.49: In Exercises 4154, find the derivative of the function.y x4 cos x
 2.50: In Exercises 4154, find the derivative of the function.y sin x x4 y
 2.51: In Exercises 4154, find the derivative of the function.
 2.52: In Exercises 4154, find the derivative of the function.
 2.53: In Exercises 4154, find the derivative of the function.
 2.54: In Exercises 4154, find the derivative of the function.
 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: The velocity of an object in meters per second is Find the velocity...
 2.60: The velocity of an automobile starting from rest is where is measur...
 2.61: In Exercises 61 66, find the second derivative of the function.
 2.62: In Exercises 61 66, find the second derivative of the function.
 2.63: In Exercises 61 66, find the second derivative of the function.
 2.64: In Exercises 61 66, find the second derivative of the function.
 2.65: In Exercises 61 66, find the second derivative of the function.
 2.66: In Exercises 61 66, find the second derivative of the function.
 2.67: In Exercises 67 and 68, show that the function satisfies the equation.
 2.68: In Exercises 67 and 68, show that the function satisfies the equation.
 2.69: In Exercises 6980, find the derivative of the functionhx x 5 x2 3 2
 2.70: In Exercises 6980, find the derivative of the functionfx x 2 1 x 5
 2.71: In Exercises 6980, find the derivative of the functionfs s 2 15 2s ...
 2.72: In Exercises 6980, find the derivative of the functionh 1 3 f
 2.73: In Exercises 6980, find the derivative of the functiony 5 cos9x 1 x
 2.74: In Exercises 6980, find the derivative of the functiony 1 cos 2x 2 ...
 2.75: In Exercises 6980, find the derivative of the functiony x 2 sin 2x 4 y
 2.76: In Exercises 6980, find the derivative of the functiony sec7 x 7 se...
 2.77: In Exercises 6980, find the derivative of the functiony 2 3 sin3 2 ...
 2.78: In Exercises 6980, find the derivative of the functionfx 3x x2 1 y
 2.79: In Exercises 6980, find the derivative of the functiony sin x x 2
 2.80: In Exercises 6980, find the derivative of the functiony cosx 1 x 1 y
 2.81: In Exercises 81 84, find the derivative of the function at the give...
 2.82: In Exercises 81 84, find the derivative of the function at the give...
 2.83: In Exercises 81 84, find the derivative of the function at the give...
 2.84: In Exercises 81 84, find the derivative of the function at the give...
 2.85: In Exercises 85 88, use a computer algebra system to find the deriv...
 2.86: In Exercises 85 88, use a computer algebra system to find the deriv...
 2.87: In Exercises 85 88, use a computer algebra system to find the deriv...
 2.88: In Exercises 85 88, use a computer algebra system to find the deriv...
 2.89: In Exercises 8992, (a) use a computer algebra system to find the de...
 2.90: In Exercises 8992, (a) use a computer algebra system to find the de...
 2.91: In Exercises 8992, (a) use a computer algebra system to find the de...
 2.92: In Exercises 8992, (a) use a computer algebra system to find the de...
 2.93: In Exercises 9396, find the second derivative of the function.
 2.94: In Exercises 9396, find the second derivative of the function.
 2.95: In Exercises 9396, find the second derivative of the function.
 2.96: In Exercises 9396, find the second derivative of the function.
 2.97: In Exercises 97100, use a computer algebra system to find the secon...
 2.98: In Exercises 97100, use a computer algebra system to find the secon...
 2.99: In Exercises 97100, use a computer algebra system to find the secon...
 2.100: In Exercises 97100, use a computer algebra system to find the secon...
 2.101: The temperature (in degrees Fahrenheit) of food in a freezer is whe...
 2.102: The emergent velocity of a liquid flowing from a hole in the bottom...
 2.103: In Exercises 103108, find by implicit differentiation
 2.104: In Exercises 103108, find by implicit differentiation
 2.105: In Exercises 103108, find by implicit differentiation
 2.106: In Exercises 103108, find by implicit differentiation
 2.107: In Exercises 103108, find by implicit differentiation
 2.108: In Exercises 103108, find by implicit differentiation
 2.109: In Exercises 109 and 110, find the equations of the tangent line an...
 2.110: In Exercises 109 and 110, find the equations of the tangent line an...
 2.111: A point moves along the curve in such a way that the value is incre...
 2.112: The edges of a cube are expanding at a rate of 8 centimeters per se...
 2.113: The cross section of a fivemeter trough is an isosceles trapezoid ...
 2.114: A rotating beacon is located 1 kilometer off a straight shoreline (...
 2.115: A sandbag is dropped from a balloon at a height of 60 meters when t...
Solutions for Chapter 2: Differentiation
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 2: Differentiation
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 115 problems in chapter 2: Differentiation have been answered, more than 44486 students have viewed full stepbystep solutions from this chapter. Chapter 2: Differentiation includes 115 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780547167022.

Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal

Binomial
A polynomial with exactly two terms

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Endpoint of an interval
A real number that represents one “end” of an interval.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Future value of an annuity
The net amount of money returned from an annuity.

Initial side of an angle
See Angle.

Nonsingular matrix
A square matrix with nonzero determinant

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Partial sums
See Sequence of partial sums.

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Regression model
An equation found by regression and which can be used to predict unknown values.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Supply curve
p = ƒ(x), where x represents production and p represents price

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Unit vector
Vector of length 1.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].

Zero matrix
A matrix consisting entirely of zeros.