 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 109654 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.

Angular speed
Speed of rotation, typically measured in radians or revolutions per unit time

Aphelion
The farthest point from the Sun in a planet’s orbit

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Cycloid
The graph of the parametric equations

Demand curve
p = g(x), where x represents demand and p represents price

Divergence
A sequence or series diverges if it does not converge

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

Horizontal component
See Component form of a vector.

Imaginary part of a complex number
See Complex number.

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Odd function
A function whose graph is symmetric about the origin (ƒ(x) = ƒ(x) for all x in the domain of f).

Polar axis
See Polar coordinate system.

Rectangular coordinate system
See Cartesian coordinate system.

Scalar
A real number.

Slope
Ratio change in y/change in x

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

Terminal side of an angle
See Angle.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.