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Math
Calculus
EBK CALCULUS EARLY TRANSCENDENTALS
Chapter 14.5, Problem 15E
Chapter 14.5, Problem 15E
BUY
EBK CALCULUS EARLY TRANSCENDENTALS
9th Edition
ISBN:
9780357687901
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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14.1 Functions Of Several Variables
14.2 Limits And Continuity
14.3 Partial Derivatives
14.4 Tangent Planes And Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives And The Gradient Vector
14.7 Maximum And Minimum Values
14.8 Lagrange Multipliers
Chapter Questions
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Problem 1E: Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and...
Problem 2E: Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and...
Problem 3E: Use the Chain Rule to find dz/dt or dw/dt. 1. z = xy3 x2y, x = t2 + 1, y = t2 1
Problem 4E: Use the Chain Rule to find dz/dt or dw/dt. 2. z=xyx+2y,x=et,y=et
Problem 5E: Use the Chain Rule to find dz/dt or dw/dt. 3. z = sin x cos y, x = t, y = 1/t
Problem 6E: Use the Chain Rule to find dz/dt or dw/dt. 4. z=1+xy, x = tan t, y = arctan t
Problem 7E: Use the Chain Rule to find dz/dt or dw/dt. 5. w = xey/z, x = t2, y = 1 t, z = 1 + 2t
Problem 8E: Use the Chain Rule to find dz/dt or dw/dt. 6. w = ln x2+y2+z2, x = sin t, y = cos t, z = tan t
Problem 9E: Find z/s and z/t in two ways: by using the Chain Rule, and by first substituting the expressions for...
Problem 10E
Problem 11E: Use the Chain Rule to find z/s and z/t. 7. z = (x y)5, x = s2t, y = st2
Problem 12E: Use the Chain Rule to find z/s and z/t. 8. z = tan1(x2 + y2), x = s ln t, y = tes
Problem 13E: Use the Chain Rule to find z/s and z/t. 9. z = ln(3x + 2y), x = s sin t, y = t cos s
Problem 14E
Problem 15E
Problem 16E
Problem 17E: Suppose f is a differentiable function of x and y , and p(t)=f(g(t),h(t)),g(2)=4,g(2)=3,h(2)=5 ,...
Problem 18E: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, u(1,2) = 5, us(1, 2) = 4,...
Problem 19E: Suppose f is a differentiable function of x and y, and g(u, v) = f(eu + sin v, eu + cos v). Use the...
Problem 20E: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r s, s2 4r). Use the table of...
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E: Use the Chain Rule to find the indicated partial derivatives. 21. z = x4 + x2y, x = s + 2t u, y =...
Problem 26E: Use the Chain Rule to find the indicated partial derivatives. 22. T=v2u+v, u = pqr, v = pqr;...
Problem 27E: Use the Chain Rule to find the indicated partial derivatives. 23. w = xy + yz + zx, x = r cos, y = r...
Problem 28E: Use the Chain Rule to find the indicated partial derivatives. 24. P=u2+v2+w2, u = xey, v = yex, w =...
Problem 29E: Use the Chain Rule to find the indicated partial derivatives. 25. N=p+qp+r, p = u + vw, q = v + uw,...
Problem 30E: Use the Chain Rule to find the indicated partial derivatives. 26. u = xety, x = 2, y = 2, t = 2;...
Problem 31E: Use Equation 5 to find dy/dx . 31. ycosx=x2+y2
Problem 32E: Use Equation 5 to find dy/dx . 32. cos(xy)=1+siny
Problem 33E: Use Equation 5 to find dy/dx . 33. tan1x2y=x+xy2
Problem 34E: Use Equation 5 to find dy/dx . 34. eysinx=x+xy
Problem 35E: Use Equations 6 to find z/x and z/y . 35. x2+2y2+3z2=1
Problem 36E
Problem 37E
Problem 38E
Problem 39E: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its...
Problem 40E
Problem 41E: The speed of sound traveling through ocean water with salinity 35 purls per thousand has been...
Problem 42E
Problem 43E
Problem 44E: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The...
Problem 45E: The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is...
Problem 46E: A manufacturer has modeled its yearly production function P (the value of its entire production, in...
Problem 47E: One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate...
Problem 48E
Problem 49E: Assume that all the given functions are differentiable. 45. If z = f (x, y), where x = r cos and y...
Problem 50E: Assume that all the given functions are differentiable. 46. If u = f(x, y), where x = es cos t and y...
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E: Homogeneous Functions A function f is called homogeneous of degree n if it satisfies the equation...
Problem 58E
Problem 59E
Problem 60E: Equation 5 is a formula for the derivative dy/dx of a function defined implicitly by an equation...
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