Partial diffrentiation HELP

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SUMMARY

The discussion focuses on solving two problems related to partial differentiation. The first problem involves demonstrating the equation Urr=(Wxx)(Fr)^2 + 2(Wxy)(Fr)(Gr)^2 + (Wx)(Frr) + (Wy)(Grr) given U=(X,Y) where X=F(R,S) and Y=G(R,S). The second problem requires proving that U(R,K)=R^n Cos(nk) satisfies the equation Urr + 1/r U + 1/(r^2) Ukk=0. Participants emphasize the importance of defining variables, particularly W in the first problem, and suggest using the chain rule for derivatives in the second problem.

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theaviator
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Partial diffrentiation...URGENT PLZ HELP

Here are the two problems...

1- If U=(X,Y) X=F(R,S) Y=G(R,S)

SHOW THAT: Urr=(Wxx) (Fr)^2 + 2(Wxy) (Fr) (Gr)^2 + (Wx) (Frr) + (Wy)+ (Grr)


2- SHOW THAT: U(R,K)=R^n Cos(nk) satisfies the equation
Urr+1/r U + 1/(r^2) Ukk=0


that's urgent please help now if u can...thanks
 
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You need to show some work before we can help you. Also, what is W in the first question? You have not defined it! For the second one, you simply take the required derivatives of U and plug then in.
 
Use the chain rule- twice.
 

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