 2.6.1: The chain rule states that the derivative of the compositionof two ...
 2.6.2: If y is a differentiable function of u, and u is a differentiablefu...
 2.6.3: Find dy/dx.(a) y = (x2 + 5)10 (b) y = 1 + 6x
 2.6.4: Find dy/dx.(a) y = sin(3x + 2) (b) y = (x2 tan x)4
 2.6.5: Suppose that f(2) = 3, f (2) = 4,g(3) = 6, andg(3) = 5. Evaluate(a)...
 2.6.6: Given the following table of values, find the indicatedderivatives ...
 2.6.7: 726 Find f (x). f(x) = (x3 + 2x)37
 2.6.8: 726 Find f (x). f(x) = (3x2 + 2x 1)6
 2.6.9: 726 Find f (x). . f(x) =x3 7x2
 2.6.10: 726 Find f (x). f(x) = 1(x5 x + 1)9
 2.6.11: 726 Find f (x). f(x) = 4(3x2 2x + 1)3
 2.6.12: 726 Find f (x). . f(x) = x3 2x + 5
 2.6.13: 726 Find f (x). f(x) =4 + 3x
 2.6.14: 726 Find f (x). f(x) = 312 + x
 2.6.15: 726 Find f (x). f(x) = sin 1x21
 2.6.16: 726 Find f (x). f(x) = tan x
 2.6.17: 726 Find f (x). f(x) = 4 cos5 x
 2.6.18: 726 Find f (x). f(x) = 4x + 5 sin4 x
 2.6.19: 726 Find f (x). f(x) = cos2(3x)
 2.6.20: 726 Find f (x). f(x) = tan4(x3)
 2.6.21: 726 Find f (x). f(x) = 2 sec2(x7)
 2.6.22: 726 Find f (x). f(x) = cos3 xx + 12
 2.6.23: 726 Find f (x). f(x) = cos(5x)
 2.6.24: 726 Find f (x). f(x) =3x sin2(4x)
 2.6.25: 726 Find f (x). f(x) = [x + csc(x3 + 3)]3
 2.6.26: 726 Find f (x). f(x) = [x4 sec(4x2 2)]4
 2.6.27: 2740 Find dy/dx. y = x3 sin2(5x)
 2.6.28: 2740 Find dy/dx. y = x tan3(x)
 2.6.29: 2740 Find dy/dx. y = x5 sec(1/x) 3
 2.6.30: 2740 Find dy/dx. y = sin xsec(3x + 1)
 2.6.31: 2740 Find dy/dx. y = cos(cos x)
 2.6.32: 2740 Find dy/dx. y = sin(tan 3x)
 2.6.33: 2740 Find dy/dx. y = cos3(sin 2x)
 2.6.34: 2740 Find dy/dx. y = 1 + csc(x2)1 cot(x2)
 2.6.35: 2740 Find dy/dx. y = (5x + 8)7 1 x6
 2.6.36: 2740 Find dy/dx. y = (x2 + x)5 sin8 x
 2.6.37: 2740 Find dy/dx. y = x 52x + 1338
 2.6.38: 2740 Find dy/dx. y =1 + x21 x2173
 2.6.39: 2740 Find dy/dx. y = (2x + 3)3(4x2 1)8
 2.6.40: 2740 Find dy/dx. y = [1 + sin3(x5)]12
 2.6.41: 4142 Use a CAS to find dy/dx. = [x sin 2x + tan4(x7)]5
 2.6.42: 4142 Use a CAS to find dy/dx. = tan42 + (7 x)3x2 + 5x3 + sin x
 2.6.43: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.44: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.45: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.46: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.47: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.48: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.49: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.50: 4350 Find an equation for the tangent line to the graph at the spec...
 2.6.51: 5154 Find d2y/dx2. y = x cos(5x) sin2 x
 2.6.52: 5154 Find d2y/dx2. y = sin(3x2)
 2.6.53: 5154 Find d2y/dx2. y = 1 + x1 x
 2.6.54: 5154 Find d2y/dx2. y = x tan 1x
 2.6.55: 5558 Find the indicated derivative. y = cot3( ); find dyd .
 2.6.56: 5558 Find the indicated derivative. =au + bcu + d6; findddu (a,b,c,...
 2.6.57: 5558 Find the indicated derivative. dd[a cos2 + b sin2 ] (a,b const...
 2.6.58: 5558 Find the indicated derivative. = csc23 y; finddxdy .
 2.6.59: (a) Use a graphing utility to obtain the graph of the functionf(x) ...
 2.6.60: (a) Use a graphing utility to obtain the graph of the functionf(x) ...
 2.6.61: 6164 TrueFalse Determine whether the statement is true or false. Ex...
 2.6.62: 6164 TrueFalse Determine whether the statement is true or false. Ex...
 2.6.63: 6164 TrueFalse Determine whether the statement is true or false. Ex...
 2.6.64: 6164 TrueFalse Determine whether the statement is true or false. Ex...
 2.6.65: If an object suspended from a spring is displaced verticallyfrom it...
 2.6.66: Find the value of the constant A so that y = A sin 3t satisfiesthe ...
 2.6.67: Use the graph of the function f in the accompanyingfigure to evaluate
 2.6.68: Using the function f in Exercise 67, evaluateddx [f(2 sin x)]x=/6
 2.6.69: The accompanying figure shows the graph of atmosphericpressure p (l...
 2.6.70: The force F (in pounds) acting at an angle with the horizontalthat ...
 2.6.71: Recall thatddx (x) = 1, x> 01, x< 0Use this result and the chain ...
 2.6.72: Use the derivative formula for sin x and the identitycos x = sin 2 ...
 2.6.73: Letf(x) =x sin1x, x = 00, x = 0(a) Show that f is continuous at x =...
 2.6.74: Letf(x) =x2 sin1x, x = 00, x = 0(a) Show that f is continuous at x ...
 2.6.75: Given the following table of values, find the indicated derivatives...
 2.6.76: Given that f (x) = 3x + 4 and g(x) = x2 1, find F(x)if F(x) = f(g(x)).
 2.6.77: Given that f (x) = xx2 + 1and g(x) = 3x 1, findF(x) if F(x) = f(g(x)).
 2.6.78: Find f (x2) if d dx [f(x2 )] = x2 .
 2.6.79: Find d dx [f(x)] if d dx [f(3x)] = 6x.
 2.6.80: Recall that a function f is even if f(x) = f(x) and oddif f(x) = f(...
 2.6.81: Draw some pictures to illustrate the results in Exercise 80,and wri...
 2.6.82: Let y = f1(u), u = f2(v), v = f3(w), and w = f4(x). Expressdy/dx in...
 2.6.83: Find a formula forddx [f(g(h(x)))]
 2.6.84: Writing The co in cosine comes from complementary,since the cosine ...
Solutions for Chapter 2.6: THE CHAIN RULE
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 2.6: THE CHAIN RULE
Get Full SolutionsChapter 2.6: THE CHAIN RULE includes 84 full stepbystep solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 84 problems in chapter 2.6: THE CHAIN RULE have been answered, more than 39815 students have viewed full stepbystep solutions from this chapter.

Annual percentage rate (APR)
The annual interest rate

Aphelion
The farthest point from the Sun in a planet’s orbit

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Base
See Exponential function, Logarithmic function, nth power of a.

Compounded monthly
See Compounded k times per year.

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

Distributive property
a(b + c) = ab + ac and related properties

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

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

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

Obtuse triangle
A triangle in which one angle is greater than 90°.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

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

Proportional
See Power function

Subtraction
a  b = a + (b)

Symmetric property of equality
If a = b, then b = a

Time plot
A line graph in which time is measured on the horizontal axis.

Xmin
The xvalue of the left side of the viewing window,.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.