POLYMER AND PETROCHEMICALDEPARTEMENT
SUBJECT:- MATHEMATIC II
PREPARED BY ASSISTANT .LECTURE: QUSAI A.MAHDI
Chain rule:-If f
yare continuous throughout an open region [R] in the (x,y)
plane and if (x,y) are differentiable functions of (t) then (w) is a
differentiable function of (t) so,
Example:-find the derivative of w=x.y,at (t=?/2)?
If x=cost ,y=sint
Solution:-=y(-sint)+xcost=sint(-sint)+cost(cost)
=-sin
Example:-find for w=xy+z , x=cost ,y=sint, z=5t at t=0?
Solution:
POLYMER AND PETROCHEMICALDEPARTEMENT
SUBJECT:- MATHEMATIC II
PREPARED BY ASSISTANT .LECTURE: QUSAI A.MAHDI
At t=0
Example:-find at t=1 for[ w=2ye
At [t=1]
Example:- Find in terms of t at t= for
?
Chain rules for two independent variables:-
Suppose that (w=f(x,y,z)) and x=g(r,s) ,y=h(r,s) and z=k(r,s)
And all four function are continuous and have continuous first partial
derivative (w.r.t)all their independent variables then (w) has partial
derivative with to(r and s )given by.
POLYMER AND PETROCHEMICALDEPARTEMENT
SUBJECT:- MATHEMATIC II
PREPARED BY ASSISTANT .LECTURE: QUSAI A.MAHDI
Example:-find ,x=r/s ,
Solution:-=1(1/s)+2(2r)+2z(2)=(1/s)+4r+4z
Example:-express
solution
POLYMER AND PETROCHEMICALDEPARTEMENT
SUBJECT:- MATHEMATIC II
PREPARED BY ASSISTANT .LECTURE: QUSAI A.MAHDI
Notes :-1)if w=f(x) and x=g(r,s) then
And
2) Suppose f(x,y) and its partial derivative f
are continuous and
equation f(x,y)=0 defined (y) as differentiable function of x than at any
point where f
Example:- find
Solution :-Example:-find
Solution:-
Example:- find
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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