 3.4.1: ?Decomposition of a Composite Function In Exercises 1–6, complete t...
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 3.4.41: ?Slope of a Tangent Line In Exercises 41 and 42, find the slope of ...
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 3.4.163: ?Finding Derivatives In Exercises 163 and 164, the graphs of f and ...
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 3.4.165: ?Doppler Effect The frequency F of a fire truck siren heard by a st...
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 3.4.176: Depreciation The value V of a machine years after it is purchased i...
 3.4.177: ?Finding a Pattern Consider the function \(f(x)=\sin \beta x\), whe...
 3.4.178: ?Conjecture Let be a differentiable function of period p.(a) Is the...
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 3.4.182: ?Proof Let be a differentiable function of x. Use the fact that \(...
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 3.4.187: ?Linear and Quadratic Approximations The linear and quadratic appro...
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 3.4.189: ?Linear and Quadratic Approximations The linear and quadratic appro...
 3.4.190: ?Linear and Quadratic Approximations The linear and quadratic appro...
 3.4.191: ?True or False? In Exercises 191–194, determine whether the stateme...
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 3.4.193: True or False? In Exercises 191–194, determine whether the statemen...
 3.4.194: ?True or False? In Exercises 191–194, determine whether the stateme...
 3.4.195: ?Let \(f(x)=a_{1} \sin x+a_{2} \sin 2 x+\cdots+a_{n} \sin n x\), wh...
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Solutions for Chapter 3.4: The Chain Rule
Full solutions for Calculus: Early Transcendental Functions  6th Edition
ISBN: 9781285774770
Solutions for Chapter 3.4: The Chain Rule
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions, edition: 6. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9781285774770. Chapter 3.4: The Chain Rule includes 196 full stepbystep solutions. Since 196 problems in chapter 3.4: The Chain Rule have been answered, more than 184376 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Augmented matrix
A matrix that represents a system of equations.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Commutative properties
a + b = b + a ab = ba

Difference identity
An identity involving a trigonometric function of u  v

Distance (on a number line)
The distance between real numbers a and b, or a  b

Hypotenuse
Side opposite the right angle in a right triangle.

Imaginary part of a complex number
See Complex number.

Interval notation
Notation used to specify intervals, pp. 4, 5.

Leading term
See Polynomial function in x.

Linear system
A system of linear equations

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Negative numbers
Real numbers shown to the left of the origin on a number line.

Octants
The eight regions of space determined by the coordinate planes.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

Range (in statistics)
The difference between the greatest and least values in a data set.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Reflexive property of equality
a = a

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.