 3.3.1: Find the derivatives of the functions in Exercises 140. y = x'  0...
 3.3.2: Find the derivatives of the functions in Exercises 140. Y = 3  0....
 3.3.3: Find the derivatives of the functions in Exercises 140. Y = x'  3...
 3.3.4: Find the derivatives of the functions in Exercises 140. yx + v7x...
 3.3.5: Find the derivatives of the functions in Exercises 140. Y = (x + 1...
 3.3.6: Find the derivatives of the functions in Exercises 140. y = (2x  ...
 3.3.7: Find the derivatives of the functions in Exercises 140. y = (rP + ...
 3.3.8: Find the derivatives of the functions in Exercises 140. y = (I _ ...
 3.3.9: Find the derivatives of the functions in Exercises 140. 9.s=I+Vi
 3.3.10: Find the derivatives of the functions in Exercises 140. s =:zvt...
 3.3.11: Find the derivatives of the functions in Exercises 140. Y = 2tan2 ...
 3.3.12: Find the derivatives of the functions in Exercises 140. y=.5i...
 3.3.13: Find the derivatives of the functions in Exercises 140. s = cos' (...
 3.3.14: Find the derivatives of the functions in Exercises 140. 14
 3.3.15: Find the derivatives of the functions in Exercises 140. s = (sec t...
 3.3.16: Find the derivatives of the functions in Exercises 140. s = csc'(1...
 3.3.17: Find the derivatives of the functions in Exercises 140. r = Y26sin6
 3.3.18: Find the derivatives of the functions in Exercises 140. r = 26Y cos 6
 3.3.19: Find the derivatives of the functions in Exercises 140. r = sin v28
 3.3.20: Find the derivatives of the functions in Exercises 140. r = sin (6...
 3.3.21: Find the derivatives of the functions in Exercises 140. Y "2x cscX
 3.3.22: Find the derivatives of the functions in Exercises 140. Y = 2Vi si...
 3.3.23: Find the derivatives of the functions in Exercises 140. y = xlf2 ...
 3.3.24: Find the derivatives of the functions in Exercises 140. Y = Vi esc...
 3.3.25: Find the derivatives of the functions in Exercises 140. Y = 5 cotx2
 3.3.26: Find the derivatives of the functions in Exercises 140. Y = x2 cot 5x
 3.3.27: Find the derivatives of the functions in Exercises 140. Y = x 2 si...
 3.3.28: Find the derivatives of the functions in Exercises 140. Y = x 2 s...
 3.3.29: Find the derivatives of the functions in Exercises 140. s= C:lf
 3.3.30: Find the derivatives of the functions in Exercises 140. .s= I15(1...
 3.3.31: Find the derivatives of the functions in Exercises 140. y = V':J
 3.3.32: Find the derivatives of the functions in Exercises 140. = ( 2Vi )2
 3.3.33: Find the derivatives of the functions in Exercises 140. y = ~X2x~ x
 3.3.34: Find the derivatives of the functions in Exercises 140. Y = 4xYx + Vi
 3.3.35: Find the derivatives of the functions in Exercises 140. r = ( sin ...
 3.3.36: Find the derivatives of the functions in Exercises 140. r = (I + S...
 3.3.37: Find the derivatives of the functions in Exercises 140. Y = (2x + I)~
 3.3.38: Find the derivatives of the functions in Exercises 140. y = 20(3x ...
 3.3.39: Find the derivatives of the functions in Exercises 140. Y = 3(5x 2...
 3.3.40: Find the derivatives of the functions in Exercises 140. Y = (3 + c...
 3.3.41: Exercises 4148, fmd dy/ dx by implicit differentiation. xy + 2x + ...
 3.3.42: Exercises 4148, fmd dy/ dx by implicit differentiation. x2 + xy + ...
 3.3.43: Exercises 4148, fmd dy/ dx by implicit differentiation. x' + 4xy ...
 3.3.44: Exercises 4148, fmd dy/ dx by implicit differentiation. 5x4/' + IO...
 3.3.45: Exercises 4148, fmd dy/ dx by implicit differentiation. ViY = I
 3.3.46: Exercises 4148, fmd dy/ dx by implicit differentiation. x"y2 = I
 3.3.47: Exercises 4148, fmd dy/ dx by implicit differentiation. Y  x + I
 3.3.48: Exercises 4148, fmd dy/ dx by implicit differentiation. y2 =~: ~ ~
 3.3.49: Exercises 49 and 50, fmddp/dq 49
 3.3.50: Exercises 49 and 50, fmddp/dq q = (5p2 + 2pt'f2
 3.3.51: Exercises 51 and 52, fmddr/ds. rcos2s + sin2 s = 1r
 3.3.52: Exercises 51 and 52, fmddr/ds. 2rs  r  S + 82 = 3
 3.3.53: Find d"y/dx 2 by implicit differentiation: a. x' + y' = I b. y2 = I...
 3.3.54: Find d"y/dx 2 by implicit differentiation: a. x' + y' = I b. y2 = I...
 3.3.55: Suppose that functions f(x) and g(x) and their first derivatives ha...
 3.3.56: Suppose that the functioo f(x) and its frrst derivative have the fo...
 3.3.57: Find the value ofdy/dt att = Oify = 3sin2xandx = t 2 + 'If.
 3.3.58: Find the value ofdy/dt att = Oify = 3sin2xandx = t 2 + 'If.
 3.3.59: Find the value of dw/ds at s = 0 if w = sin (vr  2) and r = 8sin(s...
 3.3.60: Find the value of dr/dt at t = 0 if r = (rP + 7)1/3 and rPt+6=\.
 3.3.61: Ify' + Y = 2cosx, fmdthevalue ofd"y/dx2 at the point (0, I).
 3.3.62: Ifxl/3 + yl/' = 4,findd"y/dx2 atthepoint(8,8).
 3.3.63: In Exercises 63 and 64, fmd the derivative using the defmition f(t)...
 3.3.64: In Exercises 63 and 64, fmd the derivative using the defmition g(x)...
 3.3.65: a. Graph the function { X2, f(x) = X2, b. Is f continuous at x = 0...
 3.3.66: a. Graph the function f(x) = {x' tanx, b. Is f continuous at x = 07...
 3.3.67: a. Graph the function 1:5x
 3.3.68: For what value or values of the constant m, if any, is f(x) = {Sin2...
 3.3.69: Are there any points on the curve y = (x/2) + 1/(2x  4) where the ...
 3.3.70: Are there any points on the curve y = x  1/(2x) where the slope is...
 3.3.71: Find the points on the curve y = 2x3  3x2  12x + 20 where the tan...
 3.3.72: Find the x and yintercepts of the line that is tangent to the cur...
 3.3.73: Find the points on the curve y = 2x3  3x2  12x + 20 where the tan...
 3.3.74: Show that the tangents to the curve y = ('1r sin x)/x at x = '1r an...
 3.3.75: Find the points on the curve y = tan x, '1r /2 < x < '1r /2, where...
 3.3.76: Find equations for the tangent and normal to the curve y = I + cos ...
 3.3.77: The parabola y = x 2 + C is to be tangent to the line y = x. Find C.
 3.3.78: Show that the tangent to the curve y = x 3 at any point (a, a3) mee...
 3.3.79: For what value of cis the curve y = c/(x + I) tangent to the line t...
 3.3.80: Show that the normal line at any point of the circle x2 + y2 = a2 p...
 3.3.81: In Exercises 8186, fmd equations for the lines that are tangent an...
 3.3.82: In Exercises 8186, fmd equations for the lines that are tangent an...
 3.3.83: In Exercises 8186, fmd equations for the lines that are tangent an...
 3.3.84: In Exercises 8186, fmd equations for the lines that are tangent an...
 3.3.85: In Exercises 8186, fmd equations for the lines that are tangent an...
 3.3.86: In Exercises 8186, fmd equations for the lines that are tangent an...
 3.3.87: Find the slope of the curve x3 y 3 + y2 = X + y at the points (I, I...
 3.3.88: The graph shown suggests that the curve y = sin (x  sinx) might ha...
 3.3.89: Each of the fignres in Exercises 89 and 90 shows _ graphs, the grap...
 3.3.90: Each of the fignres in Exercises 89 and 90 shows _ graphs, the grap...
 3.3.91: Use the following information to graph the function y ~ !(x) for 1...
 3.3.92: Repeat Exercise 91, supposing that the graph starts at (I, 0) inst...
 3.3.93: What is the value of the derivative of the rabbit population when t...
 3.3.94: In what units should the slopes of the rabbit and fox population cu...
 3.3.95: Find the limits in Exercises 95102.lim sin x xa 2x2  x
 3.3.96: Find the limits in Exercises 95102. lim 3x  atan 7x
 3.3.97: Find the limits in Exercises 95102. lim sinr1'0 tan2r
 3.3.98: Find the limits in Exercises 95102. lim a 90 (1
 3.3.99: Find the limits in Exercises 95102. '~(rrf2) tan26 + 5
 3.3.100: Find the limits in Exercises 95102. lim I  2 cot' 6,~o+5cot'6 7c...
 3.3.101: Find the limits in Exercises 95102. lim X sinxxa 2 2cosx
 3.3.102: Find the limits in Exercises 95102. lim I  ;os 6
 3.3.103: The lateral surface area S of a right circolar cone is related to t...
 3.3.104: The lateral surface area S of a right circolar cone is related to t...
 3.3.105: The total surface area S of a right circular cylinder is related to...
 3.3.106: The lateral surface area S of a right circolar cone is related to t...
 3.3.107: The radius of a circle is changing at the rate of 2/11" mfsec. At ...
 3.3.108: The volume of a cobe is increasing at the rate of 1200 em' /min at ...
 3.3.109: If two resistors of R, and R2 ohms are connected in parallel in an ...
 3.3.110: The impedance Z (ohms) in a series circuit is related to the resist...
 3.3.111: The coordinates of a particle moving in the metric xyplane are dif...
 3.3.112: A particle moves along the curve y = x 3 / 2 in the first quadrant ...
 3.3.113: Water drains from the conical tank shown in the accompanying figure...
 3.3.114: As television cable is pulled from a large spool to be strung from ...
 3.3.115: The figure shows a boat I km offshore, sweeping the shore with a se...
 3.3.116: Points A and B move along the x and yaxes, respectively, in such ...
 3.3.117: Find the linearizations of a. tan x atx = 7f/4 b. secx atx = 7f/4...
 3.3.118: We can obtain a useful linear approximation of the function f(x) = ...
 3.3.119: Findthelinearizationoff(x) = \I'l+x + sinx  0.5 atx = O
 3.3.120: Find the linearization of f(x) = 2/(1  x) + '\,I'l+x  3.1 atx = O
 3.3.121: Write a formula that estimates the change that occurs in the latera...
 3.3.122: a. How accurately should you measure the edge of a cube to be reaso...
 3.3.123: The circumference of the equator of a sphere is measured as 10 em w...
 3.3.124: To rmd the height of a lamppost (see accompaoying figure), you stao...
Solutions for Chapter 3: Differentiation
Full solutions for Thomas' Calculus  12th Edition
ISBN: 9780321587992
Solutions for Chapter 3: Differentiation
Get Full SolutionsThomas' Calculus was written by and is associated to the ISBN: 9780321587992. Since 124 problems in chapter 3: Differentiation have been answered, more than 11527 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Chapter 3: Differentiation includes 124 full stepbystep solutions.

Additive inverse of a real number
The opposite of b , or b

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

Cone
See Right circular cone.

Coterminal angles
Two angles having the same initial side and the same terminal side

Domain of a function
The set of all input values for a function

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Feasible points
Points that satisfy the constraints in a linear programming problem.

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

Irrational numbers
Real numbers that are not rational, p. 2.

Leading term
See Polynomial function in x.

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Nappe
See Right circular cone.

Negative angle
Angle generated by clockwise rotation.

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Real axis
See Complex plane.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Slope
Ratio change in y/change in x