 3.1: In Exercises 14, find the derivative of the function by using the d...
 3.2: In Exercises 14, find the derivative of the function by using the d...
 3.3: In Exercises 14, find the derivative of the function by using the d...
 3.4: In Exercises 14, find the derivative of the function by using the d...
 3.5: In Exercises 5 and 6, describe the values at which is differentiable.
 3.6: In Exercises 5 and 6, describe the values at which is differentiable.
 3.7: Sketch the graph of (a) Is continuous at (b) Is differentiable at E...
 3.8: Sketch the graph of (a) Is continuous at (b) Is differentiable at E...
 3.9: In Exercises 9 and 10, find the slope of the tangent line to the gr...
 3.10: In Exercises 9 and 10, find the slope of the tangent line to the gr...
 3.11: In Exercises 11 and 12, (a) find an equation of the tangent line to...
 3.12: In Exercises 11 and 12, (a) find an equation of the tangent line to...
 3.13: In Exercises 13 and 14, use the alternative form of the derivative ...
 3.14: In Exercises 13 and 14, use the alternative form of the derivative ...
 3.15: Writing In Exercises 15 and 16, the figure shows the graphs of a fu...
 3.16: Writing In Exercises 15 and 16, the figure shows the graphs of a fu...
 3.17: In Exercises 1732, find the derivative of the function. y 25
 3.18: In Exercises 1732, find the derivative of the function. y 12
 3.19: In Exercises 1732, find the derivative of the function. fx x8y
 3.20: In Exercises 1732, find the derivative of the function.
 3.21: In Exercises 1732, find the derivative of the function.
 3.22: In Exercises 1732, find the derivative of the function. ft 8t5 ht
 3.23: In Exercises 1732, find the derivative of the function. fx x 3 3x 2ft
 3.24: In Exercises 1732, find the derivative of the function. gs 4s4 5s2 fx
 3.25: In Exercises 1732, find the derivative of the function.hx 6x 33 xg
 3.26: In Exercises 1732, find the derivative of the function. fx x12 x12 hx
 3.27: In Exercises 1732, find the derivative of the function. gt 23t 2f
 3.28: In Exercises 1732, find the derivative of the function. hx 23x2 gt
 3.29: In Exercises 1732, find the derivative of the function. f 2 3 sin g
 3.30: In Exercises 1732, find the derivative of the function. g 4 cos 6hx
 3.31: In Exercises 1732, find the derivative of the function. ft 3 cos t ...
 3.32: In Exercises 1732, find the derivative of the function. gs 53 sin s...
 3.33: Vibrating String When a guitar string is plucked, it vibrates with ...
 3.34: Vertical Motion A ball is dropped from a height of 100 feet. One se...
 3.35: Vertical Motion To estimate the height of a building, a weight is d...
 3.36: Vertical Motion A bomb is dropped from an airplane at an altitude o...
 3.37: Projectile Motion A thrown ball follows a path described by (a) Ske...
 3.38: Projectile Motion The path of a projectile thrown at an angle of wi...
 3.39: Horizontal Motion The position function of a particle moving along ...
 3.40: Modeling Data The speed of a car in miles per hour and its stopping...
 3.41: In Exercises 4157, find the derivative of the function. fx 3x 2 7x ...
 3.42: In Exercises 4157, find the derivative of the function. gx x3 3xx 2...
 3.43: In Exercises 4157, find the derivative of the function. hx x sin x co
 3.44: In Exercises 4157, find the derivative of the function.
 3.45: In Exercises 4157, find the derivative of the function.
 3.46: In Exercises 4157, find the derivative of the function. x x 1x 1 fx
 3.47: In Exercises 4157, find the derivative of the function.
 3.48: In Exercises 4157, find the derivative of the function.
 3.49: In Exercises 4157, find the derivative of the function. fx 14 3x 2fx
 3.50: In Exercises 4157, find the derivative of the function.fx 93x 2 2x fx
 3.51: In Exercises 4157, find the derivative of the function. y x2cos x
 3.52: In Exercises 4157, find the derivative of the function. y sin xx2
 3.53: In Exercises 4157, find the derivative of the function.
 3.54: In Exercises 4157, find the derivative of the function.
 3.55: In Exercises 4157, find the derivative of the function. y x tan x
 3.56: In Exercises 4157, find the derivative of the function. 1 sin x1 si...
 3.57: In Exercises 4157, find the derivative of the function. y 4xex
 3.58: Acceleration The velocity of an object in meters per second is Find...
 3.59: In Exercises 5962, find the second derivative of the function. gt t...
 3.60: In Exercises 5962, find the second derivative of the function. x 12...
 3.61: In Exercises 5962, find the second derivative of the function. f 3 ...
 3.62: In Exercises 5962, find the second derivative of the function. ht 4...
 3.63: In Exercises 63 and 64, show that the function satisfies the equati...
 3.64: In Exercises 63 and 64, show that the function satisfies the equati...
 3.65: Rate of Change Determine whether there exist any values of in the i...
 3.66: Volume The radius of a right circular cylinder is given by and its ...
 3.67: In Exercises 6796, find the derivative of the function.fx 1 x 2 1 3t 1
 3.68: In Exercises 6796, find the derivative of the function.
 3.69: In Exercises 6796, find the derivative of the function. hx x 3x2 12fx
 3.70: In Exercises 6796, find the derivative of the function.
 3.71: In Exercises 6796, find the derivative of the function.
 3.72: In Exercises 6796, find the derivative of the function. h 1 3 fs
 3.73: In Exercises 6796, find the derivative of the function. y 3 cos3x 1 x
 3.74: In Exercises 6796, find the derivative of the function. y 1 cos 2x ...
 3.75: In Exercises 6796, find the derivative of the function.
 3.76: In Exercises 6796, find the derivative of the function.
 3.77: In Exercises 6796, find the derivative of the function. y x2 sin 2x4
 3.78: In Exercises 6796, find the derivative of the function. y sec7 x7 s...
 3.79: In Exercises 6796, find the derivative of the function. y 23 sin32 ...
 3.80: In Exercises 6796, find the derivative of the function.
 3.81: In Exercises 6796, find the derivative of the function. y sin xx 2
 3.82: In Exercises 6796, find the derivative of the function. y cosx 1x 1...
 3.83: In Exercises 6796, find the derivative of the function. gt t2et4y
 3.84: In Exercises 6796, find the derivative of the function. hz ez22 gt
 3.85: In Exercises 6796, find the derivative of the function.
 3.86: In Exercises 6796, find the derivative of the function.
 3.87: In Exercises 6796, find the derivative of the function. gx x2e xy
 3.88: In Exercises 6796, find the derivative of the function. f 12 e sin 2g
 3.89: In Exercises 6796, find the derivative of the function. gx ln xf
 3.90: In Exercises 6796, find the derivative of the function. hx ln xx 1x...
 3.91: In Exercises 6796, find the derivative of the function. fx xln x
 3.92: In Exercises 6796, find the derivative of the function.
 3.93: In Exercises 6796, find the derivative of the function. y 1b2 lna b...
 3.94: In Exercises 6796, find the derivative of the function. y 1b2 a bx ...
 3.95: In Exercises 6796, find the derivative of the function. y 1a ln a bxx
 3.96: In Exercises 6796, find the derivative of the function. y 1ax ba2 l...
 3.97: In Exercises 97104, use a computer algebra system to find the deriv...
 3.98: In Exercises 97104, use a computer algebra system to find the deriv...
 3.99: In Exercises 97104, use a computer algebra system to find the deriv...
 3.100: In Exercises 97104, use a computer algebra system to find the deriv...
 3.101: In Exercises 97104, use a computer algebra system to find the deriv...
 3.102: In Exercises 97104, use a computer algebra system to find the deriv...
 3.103: In Exercises 97104, use a computer algebra system to find the deriv...
 3.104: In Exercises 97104, use a computer algebra system to find the deriv...
 3.105: In Exercises 105108, find the second derivative of the function. y ...
 3.106: In Exercises 105108, find the second derivative of the function. y ...
 3.107: In Exercises 105108, find the second derivative of the function. fx...
 3.108: In Exercises 105108, find the second derivative of the function.
 3.109: In Exercises 109114, use a computer algebra system to find the seco...
 3.110: In Exercises 109114, use a computer algebra system to find the seco...
 3.111: In Exercises 109114, use a computer algebra system to find the seco...
 3.112: In Exercises 109114, use a computer algebra system to find the seco...
 3.113: In Exercises 109114, use a computer algebra system to find the seco...
 3.114: In Exercises 109114, use a computer algebra system to find the seco...
 3.115: Refrigeration The temperature of food put in a freezer is where is ...
 3.116: Fluid Flow The emergent velocity of a liquid flowing from a hole in...
 3.117: Modeling Data The atmospheric pressure decreases with increasing al...
 3.118: Tractrix A person walking along a dock drags a boat by a 10meter r...
 3.119: In Exercises 119126, use implicit differentiation to find dy/dx. x ...
 3.120: In Exercises 119126, use implicit differentiation to find dy/dx.
 3.121: In Exercises 119126, use implicit differentiation to find dy/dx. co...
 3.122: In Exercises 119126, use implicit differentiation to find dy/dx. ye...
 3.123: In Exercises 119126, use implicit differentiation to find dy/dx. x ...
 3.124: In Exercises 119126, use implicit differentiation to find dy/dx.
 3.125: In Exercises 119126, use implicit differentiation to find dy/dx. x ...
 3.126: In Exercises 119126, use implicit differentiation to find dy/dx. co...
 3.127: In Exercises 127130, find the equations of the tangent line and the...
 3.128: In Exercises 127130, find the equations of the tangent line and the...
 3.129: In Exercises 127130, find the equations of the tangent line and the...
 3.130: In Exercises 127130, find the equations of the tangent line and the...
 3.131: In Exercises 131 and 132, use logarithmic differentiation to find d...
 3.132: In Exercises 131 and 132, use logarithmic differentiation to find d...
 3.133: In Exercise 133136, find for the function and real number a.x x a 1 3
 3.134: In Exercise 133136, find for the function and real number a. fx xx ...
 3.135: In Exercise 133136, find for the function and real number a. 33 4 x...
 3.136: In Exercise 133136, find for the function and real number a.fx ln x...
 3.137: In Exercises 137142, find the derivative of the function. y tanarcs...
 3.138: In Exercises 137142, find the derivative of the function.
 3.139: In Exercises 137142, find the derivative of the function.y x arcsec x
 3.140: In Exercises 137142, find the derivative of the function.y 12 arcta...
 3.141: In Exercises 137142, find the derivative of the function. y xarcsin...
 3.142: In Exercises 137142, find the derivative of the function. x 2 < x <...
 3.143: A point moves along the curve in such a way that the value is incre...
 3.144: Surface Area The edges of a cube are expanding at a rate of 5 centi...
 3.145: Changing Depth The cross section of a 5meter trough is an isoscele...
 3.146: Linear and Angular Velocity A rotating beacon is located 1 kilomete...
 3.147: Moving Shadow A sandbag is dropped from a balloon at a height of 60...
 3.148: Geometry Consider the rectangle shown in the figure. (a) Find the a...
 3.149: In Exercises 149152, use Newtons Method to approximate any real zer...
 3.150: In Exercises 149152, use Newtons Method to approximate any real zer...
 3.151: In Exercises 149152, use Newtons Method to approximate any real zer...
 3.152: In Exercises 149152, use Newtons Method to approximate any real zer...
 3.153: In Exercises 153 and 154, use Newtons Method to approximate, to thr...
 3.154: In Exercises 153 and 154, use Newtons Method to approximate, to thr...
Solutions for Chapter 3: Differentiation
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 3: Differentiation
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245. Since 154 problems in chapter 3: Differentiation have been answered, more than 45471 students have viewed full stepbystep solutions from this chapter. Chapter 3: Differentiation includes 154 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Constraints
See Linear programming problem.

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Exponential form
An equation written with exponents instead of logarithms.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

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)

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Projection of u onto v
The vector projv u = au # vƒvƒb2v

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.

Reflection
Two points that are symmetric with respect to a lineor a point.

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Sum of an infinite series
See Convergence of a series

Wrapping function
The function that associates points on the unit circle with points on the real number line

Zero factor property
If ab = 0 , then either a = 0 or b = 0.