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Are the two answers for the two question correct

Are the two answers for the two question correct

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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Are the two answers for the two question correct

Short Answer Questions a) f(x) = x³ (3x-2) + f'(x)=(x²³(3x-2)4) = f'(x) = x ³ x = (3x-2)* + (3x-2)4 x = (x³) dx 12 (3x-2)², 3x² = f'(x) = x ²³ x 12 (3x-2)³ + (3x-2) 4 x 3x² f'(x) = 12x³ (3x-2)³ + 3(3x - 2)² 42 x = f'(x) = (2x² (3x-2) ³ + 3x² (3x-2) 4 }= MI UX b) g(x) = (xXx - 1)³ = g'(x) = ax (Ux-1)³ ) = g(x) = x (x²1²) -g'(x) = (x-1)³ × x (x ² ) - x ² x (x-1) ((x-1) 3)2 =g²(x) = (x - 1) ³ x 2√x - x ²² x 3(x-1) ² ((x-1)³)2 (x-1)³ =g'(x) = 2√x g'(x) = ((x-1)³)² 2 (x-1)³ - 3x + (x - 1)² x 207 =g'(x)= x ½ x 3(x-1)2 20x = (x-1)3 - 6x (x-1)² √x 2Jx ((x-1) ³)² (x-1) 3-6x (x-1)² = 2 2x = ((x-1)3)² =g'(x) (x-1)³-6x (x-1) 2 = (x), f= f૬(l-X)) 2x2 X ((x-1)³)² (x-1)3-6x (x-1)² 2x72 (x-1)3 -6x (x-1) ² 1/2 ((x-1) ³)² 2x =g'(x) = =g'(x) = (x-1)³ = 6x (x-1) ² 2x²² (x-1)6 =g(x)=(x-1)=(x-1-6x) 1/2 =g'(x) = -5x-1 X9-1-X =g'(x) = 2 = ¹/² (x - 1) 4 ((x-1) ³)² 2x ¹/² (x-1)²- →> 9²(x)= = 5x + ! 1/2
Transcribed Image Text:Short Answer Questions a) f(x) = x³ (3x-2) + f'(x)=(x²³(3x-2)4) = f'(x) = x ³ x = (3x-2)* + (3x-2)4 x = (x³) dx 12 (3x-2)², 3x² = f'(x) = x ²³ x 12 (3x-2)³ + (3x-2) 4 x 3x² f'(x) = 12x³ (3x-2)³ + 3(3x - 2)² 42 x = f'(x) = (2x² (3x-2) ³ + 3x² (3x-2) 4 }= MI UX b) g(x) = (xXx - 1)³ = g'(x) = ax (Ux-1)³ ) = g(x) = x (x²1²) -g'(x) = (x-1)³ × x (x ² ) - x ² x (x-1) ((x-1) 3)2 =g²(x) = (x - 1) ³ x 2√x - x ²² x 3(x-1) ² ((x-1)³)2 (x-1)³ =g'(x) = 2√x g'(x) = ((x-1)³)² 2 (x-1)³ - 3x + (x - 1)² x 207 =g'(x)= x ½ x 3(x-1)2 20x = (x-1)3 - 6x (x-1)² √x 2Jx ((x-1) ³)² (x-1) 3-6x (x-1)² = 2 2x = ((x-1)3)² =g'(x) (x-1)³-6x (x-1) 2 = (x), f= f૬(l-X)) 2x2 X ((x-1)³)² (x-1)3-6x (x-1)² 2x72 (x-1)3 -6x (x-1) ² 1/2 ((x-1) ³)² 2x =g'(x) = =g'(x) = (x-1)³ = 6x (x-1) ² 2x²² (x-1)6 =g(x)=(x-1)=(x-1-6x) 1/2 =g'(x) = -5x-1 X9-1-X =g'(x) = 2 = ¹/² (x - 1) 4 ((x-1) ³)² 2x ¹/² (x-1)²- →> 9²(x)= = 5x + ! 1/2
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