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If y=f(u) and u- g(x) then dy dy du dx du dx If y= fu) and x = g6) then dy dy/ dt dx dx/ dt Example : dy Find di =م- قسم علوم الحياة د الرياضيات - المرحلة الأولى الكورس الأول x= 21 -5 and y Sol: dy 1 dx =2 di 2x+ dx dy dy dx dy 4.x+1 8t-19. dr dx di di Example : dy Find if dx I+- y=t Sol: dy 1 dx =1+ dt dt I'+1 dy dy / dt dy +1 %3! dx dx/ di dx

If y=f(u) and u- g(x) then dy dy du dx du dx If y= fu) and x = g6) then dy dy/ dt dx dx/ dt Example : dy Find di =م- قسم علوم الحياة د الرياضيات - المرحلة الأولى الكورس الأول x= 21 -5 and y Sol: dy 1 dx =2 di 2x+ dx dy dy dx dy 4.x+1 8t-19. dr dx di di Example : dy Find if dx I+- y=t Sol: dy 1 dx =1+ dt dt I'+1 dy dy / dt dy +1 %3! dx dx/ di dx

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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KOREK TELECOMIKOREK V:YY IO %09 N ZAIN IQ bäs öeljäll - 2_5262723079620004391.PDF dy dy du If y = f(u) and u = g(x) then dx du dx Ir y= f(1) and x= e) then dy_ dy/ dt dx/ dt dx Example : dy Find dt كلية العلوم- قسم علوم الحياة محاضرات الرياضيات - المرحلة الأولى الكورس الأول x= 21 -5 and y = x' Sol: dy = 2x + dx dx -2 di dy dy dr dy - (2x+ x2=D4x+1= 8t -19. dr dx dr di Example : dy 1 if x=t+- y =t- dr Find Sol: dy 1 =1+ dt dr =D1 di 1 1+1 '+1 dy dy _ dy / dt dx dx/ dt 1 -1 -1 dx Exercises: j H.W Find dy/dx and by using chain rule ikal a 1. y = x2x2 + 3 2. y = 4x x+ v 2 3. y = 1+x 4. y = t x = 5. y = Vt2 - 4 +3, x = 3tv2t +1 个
Transcribed Image Text:KOREK TELECOMIKOREK V:YY IO %09 N ZAIN IQ bäs öeljäll - 2_5262723079620004391.PDF dy dy du If y = f(u) and u = g(x) then dx du dx Ir y= f(1) and x= e) then dy_ dy/ dt dx/ dt dx Example : dy Find dt كلية العلوم- قسم علوم الحياة محاضرات الرياضيات - المرحلة الأولى الكورس الأول x= 21 -5 and y = x' Sol: dy = 2x + dx dx -2 di dy dy dr dy - (2x+ x2=D4x+1= 8t -19. dr dx dr di Example : dy 1 if x=t+- y =t- dr Find Sol: dy 1 =1+ dt dr =D1 di 1 1+1 '+1 dy dy _ dy / dt dx dx/ dt 1 -1 -1 dx Exercises: j H.W Find dy/dx and by using chain rule ikal a 1. y = x2x2 + 3 2. y = 4x x+ v 2 3. y = 1+x 4. y = t x = 5. y = Vt2 - 4 +3, x = 3tv2t +1 个
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