 3.5.1: Write the composite function in the form . [Identify the inner func...
 3.5.2: Write the composite function in the form . [Identify the inner func...
 3.5.3: Write the composite function in the form . [Identify the inner func...
 3.5.4: Write the composite function in the form . [Identify the inner func...
 3.5.5: Write the composite function in the form . [Identify the inner func...
 3.5.6: Write the composite function in the form . [Identify the inner func...
 3.5.7: Find the derivative of the function.
 3.5.8: Find the derivative of the function.
 3.5.9: Find the derivative of the function.
 3.5.10: Find the derivative of the function.
 3.5.11: Find the derivative of the function.
 3.5.12: Find the derivative of the function.
 3.5.13: Find the derivative of the function.
 3.5.14: Find the derivative of the function.
 3.5.15: Find the derivative of the function.
 3.5.16: Find the derivative of the function.
 3.5.17: Find the derivative of the function.
 3.5.18: Find the derivative of the function.
 3.5.19: Find the derivative of the function.
 3.5.20: Find the derivative of the function.
 3.5.21: Find the derivative of the function.
 3.5.22: Find the derivative of the function.
 3.5.23: Find the derivative of the function.
 3.5.24: Find the derivative of the function.
 3.5.25: Find the derivative of the function.
 3.5.26: Find the derivative of the function.
 3.5.27: Find the derivative of the function.
 3.5.28: Find the derivative of the function.
 3.5.29: Find the derivative of the function.
 3.5.30: Find the derivative of the function.
 3.5.31: Find the derivative of the function.
 3.5.32: Find the derivative of the function.
 3.5.33: Find the derivative of the function.
 3.5.34: Find the derivative of the function.
 3.5.35: Find the derivative of the function.
 3.5.36: Find the derivative of the function.
 3.5.37: Find the derivative of the function.
 3.5.38: Find the derivative of the function.
 3.5.39: Find the derivative of the function.
 3.5.40: Find the derivative of the function.
 3.5.41: Find the derivative of the function.
 3.5.42: Find the derivative of the function.
 3.5.43: Find an equation of the tangent line to the curve at the given point
 3.5.44: Find an equation of the tangent line to the curve at the given point
 3.5.45: Find an equation of the tangent line to the curve at the given point
 3.5.46: Find an equation of the tangent line to the curve at the given point
 3.5.47: (a) Find an equation of the tangent line to the curve at the point ...
 3.5.48: (a) The curve is called a bulletnose curve. Find an equation of th...
 3.5.49: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 3.5.50: The function , , arises in applications to frequency modulation (FM...
 3.5.51: Find all points on the graph of the function at which the tangent l...
 3.5.52: Find the coordinates of all points on the curve at which the tange...
 3.5.53: Suppose that and , , , and . Find .
 3.5.54: Suppose that and , , , , , and . Find .
 3.5.55: A table of values for , , , and is given. (a) If , find . (b) If , ...
 3.5.56: Let and be the functions in Exercise 55. (a) If , find . (b) If , G...
 3.5.57: If and are the functions whose graphs are shown, let , , and . Find...
 3.5.58: If is the function whose graph is shown, let and . Use the graph of...
 3.5.59: Use the table to estimate the value of , where hx f txh0.5
 3.5.60: If , use the table to estimate the value of .
 3.5.61: Suppose is differentiable on . Let and . Find expressions for (a) a...
 3.5.62: Suppose is differentiable on and is a real number. Let and . Find e...
 3.5.63: Suppose is a function such that for . Find an expression for the de...
 3.5.64: Let , where , , , t2 5, and . Find . f 3 6 r1 rx
 3.5.65: The displacement of a particle on a vibrating string is given by p ...
 3.5.66: If the equation of motion of a particle is given by , the particle ...
 3.5.67: A Cepheid variable star is a star whose brightness alternately incr...
 3.5.68: In Example 4 in Section 1.3 we arrived at a model for the length of...
 3.5.69: The motion of a spring that is subject to a frictional force or a d...
 3.5.70: Under certain circumstances a rumor spreads according to the equati...
 3.5.71: The flash unit on a camera operates by storing charge on a capacito...
 3.5.72: The table gives the U.S. population from 1790 to 1860. (a) Use a gr...
 3.5.73: Computer algebra systems have commands that differentiate functions...
 3.5.74: (a) Use a CAS to differentiate the function and to simplify the res...
 3.5.75: Use the Chain Rule to prove the following. (a) The derivative of an...
 3.5.76: Use the Chain Rule and the Product Rule to give an alternative proo...
 3.5.77: (a) If is a positive integer, prove that (b) Find a formula for the...
 3.5.78: Suppose is a curve that always lies above the axis and never has a...
 3.5.79: Use the Chain Rule to show that if is measured in degrees, then (Th...
 3.5.80: (a) Write and use the Chain Rule to show that (b) If , find and ske...
 3.5.81: Suppose and are polynomials and is a positive integer. Use mathemat...
Solutions for Chapter 3.5: The Chain Rule
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 3.5: The Chain Rule
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Since 81 problems in chapter 3.5: The Chain Rule have been answered, more than 47422 students have viewed full stepbystep solutions from this chapter. Chapter 3.5: The Chain Rule includes 81 full stepbystep solutions. Calculus, was written by and is associated to the ISBN: 9780534393397.

Anchor
See Mathematical induction.

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

DMS measure
The measure of an angle in degrees, minutes, and seconds

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Equation
A statement of equality between two expressions.

Equilibrium price
See Equilibrium point.

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Gaussian curve
See Normal curve.

Index of summation
See Summation notation.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

kth term of a sequence
The kth expression in the sequence

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Present value of an annuity T
he net amount of your money put into an annuity.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Third quartile
See Quartile.