 3.7.1: Two equivalent forms of the Chain Rule for calculating the derivati...
 3.7.2: Let h1x2 = f 1g1x22, where f and g are differentiable on their doma...
 3.7.3: Fill in the blanks. The derivative of f 1g1x22 equals f _ evaluated...
 3.7.4: Identify the inner and outer functions in the composition cos4 x.
 3.7.5: Identify the inner and outer functions in the composition 1x2 + 1025.
 3.7.6: Express Q1x2 = cos4 1x2 + 12 as the composition of three functions;...
 3.7.7: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.8: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.9: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.10: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.11: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.12: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.13: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.14: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.15: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.16: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.17: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.18: 718. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to...
 3.7.19: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.20: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.21: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.22: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.23: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.24: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.25: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.26: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.27: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.28: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.29: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.30: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.31: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.32: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.33: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.34: 1934. Version 2 of the Chain Rule Use Version 2 of the Chain Rule t...
 3.7.35: 3536. Similarlooking composite functions Two composite functions a...
 3.7.36: 3536. Similarlooking composite functions Two composite functions a...
 3.7.37: Chain Rule using a table Let h1x2 = f 1g1x22 and p1x2 = g1 f 1x22. ...
 3.7.38: Chain Rule using a table Let h1x2 = f 1g1x22 and k1x2 = g1g1x22. Us...
 3.7.39: Applying the Chain Rule Use the data in Tables 3.4 and 3.5 of Examp...
 3.7.40: Changing temperature The lapse rate is the rate at which the temper...
 3.7.41: 4144. Chain Rule for powers Use the Chain Rule to find the derivati...
 3.7.42: 4144. Chain Rule for powers Use the Chain Rule to find the derivati...
 3.7.43: 4144. Chain Rule for powers Use the Chain Rule to find the derivati...
 3.7.44: 4144. Chain Rule for powers Use the Chain Rule to find the derivati...
 3.7.45: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.46: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.47: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.48: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.49: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.50: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.51: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.52: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.53: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.54: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.55: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.56: 4556. Repeated use of the Chain Rule Calculate the derivative of th...
 3.7.57: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.58: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.59: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.60: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.61: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.62: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.63: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.64: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.65: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.66: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.67: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.68: 5768. Combining rules Use the Chain Rule combined with other differ...
 3.7.69: Explain why or why not Determine whether the following statements a...
 3.7.70: 7073. Second derivatives Find d2y dx2 for the following functions. ...
 3.7.71: 7073. Second derivatives Find d2y dx2 for the following functions. ...
 3.7.72: 7073. Second derivatives Find d2y dx2 for the following functions. ...
 3.7.73: 7073. Second derivatives Find d2y dx2 for the following functions. ...
 3.7.74: Derivatives by different methods a. Calculate d dx 1x2 + x22 using ...
 3.7.75: 7576. Square root derivatives Find the derivative of the following ...
 3.7.76: 7576. Square root derivatives Find the derivative of the following ...
 3.7.77: Tangent lines Determine an equation of the line tangent to the grap...
 3.7.78: Tangent lines Determine equations of the lines tangent to the graph...
 3.7.79: Tangent lines Assume f and g are differentiable on their domains wi...
 3.7.80: Tangent lines Assume f is a differentiable function whose graph pas...
 3.7.81: Tangent lines Find the equation of the line tangent to y = e2x at x...
 3.7.82: Composition containing sin x Suppose f is differentiable on 32, 24...
 3.7.83: Composition containing sin x Suppose f is differentiable for all re...
 3.7.84: Use equation (2) to answer the following questions. a. Find dy dt ,...
 3.7.85: Use equation (2) to answer the following questions. a. Find the sec...
 3.7.86: Use equation (2) to answer the following questions. a. The period T...
 3.7.87: A damped oscillator The displacement of a mass on a spring suspende...
 3.7.88: Oscillator equation A mechanical oscillator (such as a mass on a sp...
 3.7.89: Hours of daylight The number of hours of daylight at any point on E...
 3.7.90: A mixing tank A 500liter (L) tank is filled with pure water. At ti...
 3.7.91: Power and energy The total energy in megawatthr (MWh) used by a to...
 3.7.92: Deriving trigonometric identities a. Differentiate both sides of th...
 3.7.93: Proof of cos2 x _ sin2 x _ 1 Let f 1x2 = cos2 x + sin2 x. a. Use th...
 3.7.94: Using the Chain Rule to prove that d dx 1ekx 2 _ kekx a. Identify t...
 3.7.95: Deriving the Quotient Rule using the Product Rule and Chain Rule Su...
 3.7.96: The Chain Rule for second derivatives a. Derive a formula for the s...
 3.7.97: 97100. Calculating limits The following limits are the derivatives ...
 3.7.98: 97100. Calculating limits The following limits are the derivatives ...
 3.7.99: 97100. Calculating limits The following limits are the derivatives ...
 3.7.100: 97100. Calculating limits The following limits are the derivatives ...
 3.7.101: Limit of a difference quotient Assuming that f is differentiable fo...
 3.7.102: Derivatives of even and odd functions Recall that f is even if f 1...
 3.7.103: A general proof of the Chain Rule Let f and g be differentiable fun...
Solutions for Chapter 3.7: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 3.7
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.7 includes 103 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Since 103 problems in chapter 3.7 have been answered, more than 57131 students have viewed full stepbystep solutions from this chapter.

Binomial
A polynomial with exactly two terms

Common difference
See Arithmetic sequence.

Dependent event
An event whose probability depends on another event already occurring

Direction vector for a line
A vector in the direction of a line in threedimensional space

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Graphical model
A visible representation of a numerical or algebraic model.

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

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

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

Ordered pair
A pair of real numbers (x, y), p. 12.

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

Parametric curve
The graph of parametric equations.

Period
See Periodic function.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Random variable
A function that assigns realnumber values to the outcomes in a sample space.

Spiral of Archimedes
The graph of the polar curve.

Sum of an infinite series
See Convergence of a series

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

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.