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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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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