X=x( p,q,s), y=y(p,u,v), s=s(u,v), p=p(t) will be 2. The second order partial derivatives Fxx(x,y) of the function ( F(x,y) =x*y - In (x²-y) ) equal . 3. The differential of the following function ( Z = X' Sin (6Y) ) is equal .. ..........

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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Q3: Fill in the blanks in the following:
1. The tree diagram of the Chain Rule for the given function w=w(x,y),
X=x( p,q,s), y=y(p,u,v) , s=s(u,v), p=p(t) will be .
2. The second order partial derivatives Fxx(x,y) of the function ( F(x,y) =x*y-
In (x²-y) ) equal .
3. The differential of the following function ( Z = x² Sin (6Y) ) is equal
4. The integration form of Sf, XY dA where D is the portion of X? + Y? = 2 in
the 1" quadrant will be .
5. The type of roots of the 2nd order differential equation [y-4y - 12y = 0]
is .
Transcribed Image Text:Q3: Fill in the blanks in the following: 1. The tree diagram of the Chain Rule for the given function w=w(x,y), X=x( p,q,s), y=y(p,u,v) , s=s(u,v), p=p(t) will be . 2. The second order partial derivatives Fxx(x,y) of the function ( F(x,y) =x*y- In (x²-y) ) equal . 3. The differential of the following function ( Z = x² Sin (6Y) ) is equal 4. The integration form of Sf, XY dA where D is the portion of X? + Y? = 2 in the 1" quadrant will be . 5. The type of roots of the 2nd order differential equation [y-4y - 12y = 0] is .
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