 14.5.1: Use the Chain Rule to find or .
 14.5.2: Use the Chain Rule to find or .
 14.5.3: Use the Chain Rule to find or .
 14.5.4: Use the Chain Rule to find or .
 14.5.5: Use the Chain Rule to find or .
 14.5.6: Use the Chain Rule to find or .
 14.5.7: Use the Chain Rule to find and
 14.5.8: Use the Chain Rule to find and
 14.5.9: Use the Chain Rule to find and
 14.5.10: Use the Chain Rule to find and
 14.5.11: Use the Chain Rule to find and
 14.5.12: Use the Chain Rule to find and
 14.5.13: If z fx, y f x where f is differentiable, x tt y ht t3 2 t3 5 h3 7 ...
 14.5.14: Let Ws, t Fus, t, vs, t F, u, and, where are differentiable, u1, 0 ...
 14.5.15: Suppose is a differentiable function of and , and . Use the table o...
 14.5.16: Suppose is a differentiable function of and , and Use the table of ...
 14.5.17: Use a tree diagram to write out the Chain Rule for the given case. ...
 14.5.18: Use a tree diagram to write out the Chain Rule for the given case. ...
 14.5.19: Use a tree diagram to write out the Chain Rule for the given case. ...
 14.5.20: Use a tree diagram to write out the Chain Rule for the given case. ...
 14.5.21: Use the Chain Rule to find the indicated partial derivatives. z x 2...
 14.5.22: Use the Chain Rule to find the indicated partial derivatives. u sr ...
 14.5.23: Use the Chain Rule to find the indicated partial derivatives. R lnu...
 14.5.24: Use the Chain Rule to find the indicated partial derivatives. M xe ...
 14.5.25: Use the Chain Rule to find the indicated partial derivatives. u x x...
 14.5.26: Use the Chain Rule to find the indicated partial derivatives. Y w t...
 14.5.27: Use Equation 6 to find dydx
 14.5.28: Use Equation 6 to find dydx
 14.5.29: Use Equation 6 to find dydx
 14.5.30: Use Equation 6 to find dydx
 14.5.31: Use Equations 7 to find and zx zy
 14.5.32: Use Equations 7 to find and zx zy
 14.5.33: Use Equations 7 to find and zx zy
 14.5.34: Use Equations 7 to find and zx zy
 14.5.35: The temperature at a point is , measured in degrees Celsius. A bug ...
 14.5.36: Wheat production in a given year, , depends on the average temperat...
 14.5.37: The speed of sound traveling through ocean water with salinity 35 p...
 14.5.38: The radius of a right circular cone is increasing at a rate of ins ...
 14.5.39: The length , width , and height of a box change with time. At a cer...
 14.5.40: The voltage in a simple electrical circuit is slowly decreasing as ...
 14.5.41: The pressure of 1 mole of an ideal gas is increasing at a rate of k...
 14.5.42: Car A is traveling north on Highway 16 and car B is traveling west ...
 14.5.43: Assume that all the given functions are differentiable. If , where ...
 14.5.44: Assume that all the given functions are differentiable. If , where ...
 14.5.45: Assume that all the given functions are differentiable. If , s zxzy
 14.5.46: Assume that all the given functions are differentiable. If , where ...
 14.5.47: Assume that all the given functions have continuous secondorder pa...
 14.5.48: Assume that all the given functions have continuous secondorder pa...
 14.5.49: Assume that all the given functions have continuous secondorder pa...
 14.5.50: Assume that all the given functions have continuous secondorder pa...
 14.5.51: Assume that all the given functions have continuous secondorder pa...
 14.5.52: Assume that all the given functions have continuous secondorder pa...
 14.5.53: A function f is called homogeneous of degree n if it satisfies the ...
 14.5.54: If is homogeneous of degree , show that x2 2 f x 2 2xy 2 f x y y 2 ...
 14.5.55: If is homogeneous of degree , show that fxtx, ty tn1fxx, y(b)
 14.5.56: Suppose that the equation implicitly defines each of the three vari...
Solutions for Chapter 14.5: The Chain Rule
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 14.5: The Chain Rule
Get Full SolutionsCalculus, was written by and is associated to the ISBN: 9780534393397. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Since 56 problems in chapter 14.5: The Chain Rule have been answered, more than 43786 students have viewed full stepbystep solutions from this chapter. Chapter 14.5: The Chain Rule includes 56 full stepbystep solutions.

Axis of symmetry
See Line of symmetry.

Bearing
Measure of the clockwise angle that the line of travel makes with due north

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

Data
Facts collected for statistical purposes (singular form is datum)

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Endpoint of an interval
A real number that represents one “end” of an interval.

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Geometric series
A series whose terms form a geometric sequence.

Imaginary axis
See Complex plane.

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

Index of summation
See Summation notation.

Logarithmic form
An equation written with logarithms instead of exponents

Monomial function
A polynomial with exactly one term.

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

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

Variance
The square of the standard deviation.