Math Is Fun Forum

malsch

Member

Registered: 2012-12-15

Posts: 2

Partial Derivatives

Hi, I have a function f(x,y). u = ax + by and v = bx - ay. a and b are constants. i need to prove that d2f/du2 + d2f/dv2 = 0.

I have started out by finding df/du using chain rule:

df/du = df/dx * dx/du + df/dy * dy/du

Hence, df/du = df/a*dx + df/b*dy

My problem is that now i need to find d^2f/du^2 but i do not know how to continue from df/du (ie. i do not know how i can differentiate df/a*dx + df/b*dy with respect to u).

Thanks for reading

Last edited by malsch (2012-12-15 23:12:24)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Partial Derivatives

You said ". i need to prove that d2f/dx2 + d2f/dv2 = 0.".
I see f, x, f, v, but no u, why no u ?

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igloo myrtilles fourmis

malsch

Member

Registered: 2012-12-15

Posts: 2

Re: Partial Derivatives

sorry i miswrote dx2 instead of du2. i've edited the post