# Proving a Partial Derivative

1. Feb 2, 2012

### xortan

1. The problem statement, all variables and given/known data
I have attached a picture of the problem. The question is the first one.

2. Relevant equations

3. The attempt at a solution
I tried subbing u and v into the right hand side of the equation. I expanded and simplified but I do not think that is the right way to go about it. If somebody can point me in the right direction that would be very helpful. Thank you!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Feb 2, 2012

### tiny-tim

hi xortan!
my guess is that it's quicker to start from the left hand side

(you could also "factor" it into (∂/∂x + ∂/∂y)(∂/∂x - ∂/∂y)z)

… show us what you get

3. Feb 2, 2012

### xortan

Well I am really new at partial derivative, we just started this course. Was doing a single variable calc course last semester and only touched on this stuff briefly at the end. I am not understanding where to go when starting from the left hand side. I asked another one of my instructors and he showed me this "brute force" way of doing it. I got it to a point of

(∂2z/∂x2 = (∂/∂x)(∂z/∂u)2x + ∂z/∂u * 2 + (∂/∂x)(∂z/∂v)2y

I got to deal with the first term now but the question seems to be blowing up and I know there has to be an easier way of doing this