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Co 59-62 Verify that the conclusion of Clairaut's Theorem holds, that is, Uxy = Uyx- 59. u = x+y³y4 61. u = cos(x²y) 63-70 Find the indicated partial derivative(s). 63. f(x, y) = x¹y² – x³y; fxxx, fxyx - 64. f(x, y) = sin(2x + 5y); fyxy 65. f(x, y, z) = xyz²; fxyz 66. g(r, s, t) = e' sin(st); grst 67. W = √√√u + v²; a³w du² dv √I + uv² 3xx 60. u = et sin y 62. u = ln(x + 2y)

Co 59-62 Verify that the conclusion of Clairaut's Theorem holds, that is, Uxy = Uyx- 59. u = x+y³y4 61. u = cos(x²y) 63-70 Find the indicated partial derivative(s). 63. f(x, y) = x¹y² – x³y; fxxx, fxyx - 64. f(x, y) = sin(2x + 5y); fyxy 65. f(x, y, z) = xyz²; fxyz 66. g(r, s, t) = e' sin(st); grst 67. W = √√√u + v²; a³w du² dv √I + uv² 3xx 60. u = et sin y 62. u = ln(x + 2y)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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61,67
1 dt 51. (a) 52. (a) z=f(x)g(y) (c) z = f(x/y) 55. z = 53-58 Find all the second partial derivatives. 53. f(x, y) = xy - 2x³y² y 2x + 3y 57. v= = sin(s² - t²) 67. W = g(y) 69. w= √u + v²; 59-62 Verify that the conclusion of Clairaut's Theorem holds, that is, Uxy = Uyx- 59. u = x²y³ - y4 61. u = cos(x²y) 63-70 Find the indicated partial derivative(s). 63. f(x, y) = x²y² - x³y; fxxx, fryx 64. f(x, y) = sin(2x + 5y); fyxy 65. f(x, y, z) = exy²²2; fxyz 66. g(r, s, t) = e' sin(st); grst 68. V = ln(r + s² + t³); X 9 y + 2z' (b) z=f(x + y) (b) z = f(xy) a³w du² dv 54. f(x, y) = In(ax + by) 56. Ter cos 0 2³ ər əs Ət 58. w = √+² 60. u = ex sin y 62. u = ln(x + 2y) d³ w J³w az ay əx' ax² dy 74. Level cur the follow point P. (a) f 75. Verify heat c 76. Deter soluti (a) (c) L (e) L 77. Veri the t 78. Show wav (a) (c) (d) 79. If ab is
Transcribed Image Text:1 dt 51. (a) 52. (a) z=f(x)g(y) (c) z = f(x/y) 55. z = 53-58 Find all the second partial derivatives. 53. f(x, y) = xy - 2x³y² y 2x + 3y 57. v= = sin(s² - t²) 67. W = g(y) 69. w= √u + v²; 59-62 Verify that the conclusion of Clairaut's Theorem holds, that is, Uxy = Uyx- 59. u = x²y³ - y4 61. u = cos(x²y) 63-70 Find the indicated partial derivative(s). 63. f(x, y) = x²y² - x³y; fxxx, fryx 64. f(x, y) = sin(2x + 5y); fyxy 65. f(x, y, z) = exy²²2; fxyz 66. g(r, s, t) = e' sin(st); grst 68. V = ln(r + s² + t³); X 9 y + 2z' (b) z=f(x + y) (b) z = f(xy) a³w du² dv 54. f(x, y) = In(ax + by) 56. Ter cos 0 2³ ər əs Ət 58. w = √+² 60. u = ex sin y 62. u = ln(x + 2y) d³ w J³w az ay əx' ax² dy 74. Level cur the follow point P. (a) f 75. Verify heat c 76. Deter soluti (a) (c) L (e) L 77. Veri the t 78. Show wav (a) (c) (d) 79. If ab is
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