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## #1 2012-12-16 00:36:52

malsch
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### 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).

Last edited by malsch (2012-12-16 22:12:24)

## #2 2012-12-16 04:47:26

John E. Franklin
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### 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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## #3 2012-12-16 22:13:17

malsch
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### Re: Partial Derivatives

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