 13.5.1: In Exercises 14, find using the appropriate Chain Rule
 13.5.2: In Exercises 14, find using the appropriate Chain Rule
 13.5.3: In Exercises 14, find using the appropriate Chain Rule
 13.5.4: In Exercises 14, find using the appropriate Chain Rule
 13.5.5: In Exercises 510, find (a) by using the appropriate Chain Rule and ...
 13.5.6: In Exercises 510, find (a) by using the appropriate Chain Rule and ...
 13.5.7: In Exercises 510, find (a) by using the appropriate Chain Rule and ...
 13.5.8: In Exercises 510, find (a) by using the appropriate Chain Rule and ...
 13.5.9: In Exercises 510, find (a) by using the appropriate Chain Rule and ...
 13.5.10: In Exercises 510, find (a) by using the appropriate Chain Rule and ...
 13.5.11: Projectile Motion In Exercises 11 and 12, the parametric equations ...
 13.5.12: Projectile Motion In Exercises 11 and 12, the parametric equations ...
 13.5.13: In Exercises 13 and 14, find using the appropriate Chain Rule. Eval...
 13.5.14: In Exercises 13 and 14, find using the appropriate Chain Rule. Eval...
 13.5.15: In Exercises 1518, find and using the appropriate Chain Rule, and e...
 13.5.16: In Exercises 1518, find and using the appropriate Chain Rule, and e...
 13.5.17: In Exercises 1518, find and using the appropriate Chain Rule, and e...
 13.5.18: In Exercises 1518, find and using the appropriate Chain Rule, and e...
 13.5.19: In Exercises 1922, find and (a) by using the appropriate Chain Rule...
 13.5.20: In Exercises 1922, find and (a) by using the appropriate Chain Rule...
 13.5.21: In Exercises 1922, find and (a) by using the appropriate Chain Rule...
 13.5.22: In Exercises 1922, find and (a) by using the appropriate Chain Rule...
 13.5.23: In Exercises 2326, find and by using the appropriate Chain Rule.w x...
 13.5.24: In Exercises 2326, find and by using the appropriate Chain Rule.
 13.5.25: In Exercises 2326, find and by using the appropriate Chain Rule.w z...
 13.5.26: In Exercises 2326, find and by using the appropriate Chain Rule.w x...
 13.5.27: In Exercises 2730, differentiate implicitly to find dy/dx.x2 xy y2 ...
 13.5.28: In Exercises 2730, differentiate implicitly to find dy/dx.sec xy ta...
 13.5.29: In Exercises 2730, differentiate implicitly to find dy/dx.lnx2 y2 x...
 13.5.30: In Exercises 2730, differentiate implicitly to find dy/dx.xx2 y2 y2 6
 13.5.31: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.32: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.33: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.34: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.35: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.36: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.37: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.38: In Exercises 3138, differentiate implicitly to find the first parti...
 13.5.39: In Exercises 39 42, differentiate implicitly to find the first part...
 13.5.40: In Exercises 39 42, differentiate implicitly to find the first part...
 13.5.41: In Exercises 39 42, differentiate implicitly to find the first part...
 13.5.42: In Exercises 39 42, differentiate implicitly to find the first part...
 13.5.43: Homogeneous Functions A function is homogeneous of degree if In Exe...
 13.5.44: Homogeneous Functions A function is homogeneous of degree if In Exe...
 13.5.45: Homogeneous Functions A function is homogeneous of degree if In Exe...
 13.5.46: Homogeneous Functions A function is homogeneous of degree if In Exe...
 13.5.47: Let and where and are differentiable. Use the appropriate Chain Rul...
 13.5.48: Let and where and are differentiable. Use the appropriate Chain Rul...
 13.5.49: Let be a function in which and are functions of a single variable G...
 13.5.50: Let be a function in which and are functions of two variables and G...
 13.5.51: If give the rule for finding implicitly. If give the rule for findi...
 13.5.52: Consider the function where and (a) Use the appropriate Chain Rule ...
 13.5.53: Volume and Surface Area The radius of a right circular cylinder is ...
 13.5.54: . Volume and Surface Area Repeat Exercise 53 for a right circular cone
 13.5.55: Ideal Gas Law The Ideal Gas Law is where is a constant, is a consta...
 13.5.56: Area Let be the angle between equal sides of an isosceles triangle ...
 13.5.57: Moment of Inertia An annular cylinder has an inside radius of and a...
 13.5.58: Volume and Surface Area The two radii of the frustum of a right cir...
 13.5.59: Show that $w$u $w$v 0 w fx, y,
 13.5.60: Demonstrate the result of Exercise 59 for w x y sin y x.
 13.5.61: Consider the function where and Verify each of the following.
 13.5.62: Demonstrate the result of Exercise 61(b) for w arctan yx.
 13.5.63: CauchyRiemann Equations Given the functions and verify that the Ca...
 13.5.64: Demonstrate the result of Exercise 63 for the functions u lnx . 2 y...
 13.5.65: Show that if is homogeneous of degree then [Hint: Let Find and then...
Solutions for Chapter 13.5: Chain Rules for Functions of Several Variables
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 13.5: Chain Rules for Functions of Several Variables
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.5: Chain Rules for Functions of Several Variables includes 65 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780547167022. Since 65 problems in chapter 13.5: Chain Rules for Functions of Several Variables have been answered, more than 64323 students have viewed full stepbystep solutions from this chapter.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Arcsine function
See Inverse sine function.

Chord of a conic
A line segment with endpoints on the conic

Domain of validity of an identity
The set of values of the variable for which both sides of the identity are defined

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Equivalent systems of equations
Systems of equations that have the same solution.

Exponent
See nth power of a.

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Real zeros
Zeros of a function that are real numbers.

Root of a number
See Principal nth root.

Scatter plot
A plot of all the ordered pairs of a twovariable data set on a coordinate plane.

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Third quartile
See Quartile.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].