 2.3.1: In each part, determine f (x).(a) f(x) = 6 (b) f(x) = 6x(c) f(x) = ...
 2.3.2: In parts (a)(d), determine f (x).(a) f(x) = x3 + 5 (b) f(x) = x2(x3...
 2.3.3: The slope of the tangent line to the curve y = x2 + 4x + 7at x = 1 ...
 2.3.4: If f(x) = 3x3 3x2 + x + 1, then f (x) =
 2.3.5: 18 Find dy/dx. y = 3
 2.3.6: 18 Find dy/dx. = 2x + (1/2)
 2.3.7: 18 Find dy/dx. y = 13 (x7 + 2x 9)
 2.3.8: 18 Find dy/dx. y = x2 + 15
 2.3.9: 916 Find f (x). f(x) = x3 +1x7
 2.3.10: 916 Find f (x). f(x) = x +1x
 2.3.11: 916 Find f (x). f(x) = 3x8 + 2x
 2.3.12: 916 Find f (x). f(x) = 7x6 5x
 2.3.13: 916 Find f (x). f(x) = xe +1x10
 2.3.14: 916 Find f (x). f(x) = 3 8x
 2.3.15: 916 Find f (x). f(x) = (3x2 + 1)2
 2.3.16: 916 Find f (x). f(x) = ax3 + bx2 + cx + d (a, b, c, d constant)
 2.3.17: 1718 Find y (1). y = 5x2 3x + 1
 2.3.18: 1718 Find y (1). y = x3/2 + 2x
 2.3.19: 1920 Find dx/dt. x = t 2 t
 2.3.20: 1920 Find dx/dt. x = t 2 + 13t
 2.3.21: 2124 Find dy/dxx=1. y = 1 + x + x2 + x3 + x4 + x5
 2.3.22: 2124 Find dy/dxx=1. y = 1 + x + x2 + x3 + x4 + x5 + x6x3
 2.3.23: 2124 Find dy/dxx=1. y = (1 x)(1 + x)(1 + x2)(1 + x4)
 2.3.24: 2124 Find dy/dxx=1. = x24 + 2x12 + 3x8 + 4x6
 2.3.25: 2526 Approximate f (1) by considering the difference quotientf(1 + ...
 2.3.26: 2526 Approximate f (1) by considering the difference quotientf(1 + ...
 2.3.27: 2728 Use a graphing utility to estimate the value of f (1) by zoomi...
 2.3.28: 2728 Use a graphing utility to estimate the value of f (1) by zoomi...
 2.3.29: 2932 Find the indicated derivative. ddt [16t2]
 2.3.30: 2932 Find the indicated derivative. dCdr , where C = 2r
 2.3.31: 2932 Find the indicated derivative. V (r), where V = r3
 2.3.32: 2932 Find the indicated derivative. dd [21 + ]
 2.3.33: 3336 TrueFalse Determine whether the statement is true or false. Ex...
 2.3.34: 3336 TrueFalse Determine whether the statement is true or false. Ex...
 2.3.35: 3336 TrueFalse Determine whether the statement is true or false. Ex...
 2.3.36: 3336 TrueFalse Determine whether the statement is true or false. Ex...
 2.3.37: A spherical balloon is being inflated.(a) Find a general formula fo...
 2.3.38: Finddd 0 + 62 0(0 is constant).
 2.3.39: Find an equation of the tangent line to the graph of y = f(x)at x =...
 2.3.40: Find an equation of the tangent line to the graph of y = f(x)at x =...
 2.3.41: 4142 Find d2y/dx2. (a) y = 7x3 5x2 + x (b) y = 12x2 2x + 3(c) y = x...
 2.3.42: 4142 Find d2y/dx2. (a) y = 4x7 5x3 + 2x (b) y = 3x + 2(c) y = 3x 25...
 2.3.43: 4344 Find y. (a) y = x5 + x5 (b) y = 1/x(c) y = ax3 + bx + c (a, b,...
 2.3.44: 4344 Find y. (a) y = 5x2 4x + 7 (b) y = 3x2 + 4x1 + x(c) y = ax4 + ...
 2.3.45: Find(a) f (2), where f(x) = 3x2 2(b)d2ydx2x=1, where y = 6x5 4x2(c)...
 2.3.46: Find(a) y(0), where y = 4x4 + 2x3 + 3(b)d4ydx4x=1, where y = 6x4 .
 2.3.47: Show that y = x3 + 3x + 1 satisfies y + xy 2y = 0.
 2.3.48: Show that if x = 0, then y = 1/x satisfies the equationx3y + x2y xy...
 2.3.49: 4950 Use a graphing utility to make rough estimates of the location...
 2.3.50: 4950 Use a graphing utility to make rough estimates of the location...
 2.3.51: Find a function y = ax2 + bx + c whose graph has anxintercept of 1...
 2.3.52: Find k if the curve y = x2 + k is tangent to the liney = 2x
 2.3.53: Find the xcoordinate of the point on the graph of y = x2where the ...
 2.3.54: Find the xcoordinate of the point on the graph ofy = x where the t...
 2.3.55: Find the coordinates of all points on the graph ofy = 1 x2 at which...
 2.3.56: Show that any two tangent lines to the parabola y = ax2,a = 0, inte...
 2.3.57: Suppose that L is the tangent line at x = x0 to the graph ofthe cub...
 2.3.58: Show that the segment of the tangent line to the graph ofy = 1/x th...
 2.3.59: Show that the triangle that is formed by any tangent line tothe gra...
 2.3.60: Find conditions on a, b, c, and d so that the graph of thepolynomia...
 2.3.61: Newtons Law of Universal Gravitation states that the magnitudeF of ...
 2.3.62: In the temperature range between 0C and 700C the resistanceR [in oh...
 2.3.63: 6364 Use a graphing utility to make rough estimates of the interval...
 2.3.64: 6364 Use a graphing utility to make rough estimates of the interval...
 2.3.65: 6568 You are asked in these exercises to determine whether a piecew...
 2.3.66: 6568 You are asked in these exercises to determine whether a piecew...
 2.3.67: 6568 You are asked in these exercises to determine whether a piecew...
 2.3.68: 6568 You are asked in these exercises to determine whether a piecew...
 2.3.69: Find all points where f fails to be differentiable. Justifyyour ans...
 2.3.70: In each part, compute f , f , f , and then state the formulafor f (...
 2.3.71: (a) Prove:d2dx2 [cf(x)] = c d2dx2 [f(x)]d2dx2 [f(x) + g(x)] =d2dx2 ...
 2.3.72: Let f(x) = x8 2x + 3; findlimw2f (w) f (2)w 2
 2.3.73: (a) Find f (n)(x) if f(x) = xn, n = 1, 2, 3,....(b) Find f (n)(x) i...
 2.3.74: (a) Prove: If f (x) exists for each x in (a, b), then both fand f a...
 2.3.75: Let f(x) = (mx + b)n, where m and b are constants and nis an intege...
 2.3.76: 7677 Verify the result of Exercise 75 for f(x). f(x) = (2x + 3)2
 2.3.77: 7677 Verify the result of Exercise 75 for f(x). f(x) = (3x 1)3
 2.3.78: 7881 Use the result of Exercise 75 to compute the derivative of the...
 2.3.79: 7881 Use the result of Exercise 75 to compute the derivative of the...
 2.3.80: 7881 Use the result of Exercise 75 to compute the derivative of the...
 2.3.81: 7881 Use the result of Exercise 75 to compute the derivative of the...
 2.3.82: The purpose of this exercise is to extend the power rule(Theorem 2....
Solutions for Chapter 2.3: INTRODUCTION TO TECHNIQUES OF DIFFERENTIATION
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 2.3: INTRODUCTION TO TECHNIQUES OF DIFFERENTIATION
Get Full SolutionsSince 82 problems in chapter 2.3: INTRODUCTION TO TECHNIQUES OF DIFFERENTIATION have been answered, more than 40021 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Chapter 2.3: INTRODUCTION TO TECHNIQUES OF DIFFERENTIATION includes 82 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691.

Census
An observational study that gathers data from an entire population

Combination
An arrangement of elements of a set, in which order is not important

Cubic
A degree 3 polynomial function

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Focus, foci
See Ellipse, Hyperbola, Parabola.

Function
A relation that associates each value in the domain with exactly one value in the range.

Horizontal shrink or stretch
See Shrink, stretch.

Normal curve
The graph of ƒ(x) = ex2/2

Parallel lines
Two lines that are both vertical or have equal slopes.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

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.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Stem
The initial digit or digits of a number in a stemplot.

Sum identity
An identity involving a trigonometric function of u + v

Terminal point
See Arrow.

Triangular form
A special form for a system of linear equations that facilitates finding the solution.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.

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

xintercept
A point that lies on both the graph and the xaxis,.