Correcting Mistakes in Partial Differential Equations

[aruwin]

I have calculated 3 times and I still don't get the answer. The answer should be 0.
Here's the question and my work. Which part am I wrong?


f(x,y) = 1/√(1-2xy+y^2)

Prove that ∂/∂x{(1-x^2)*∂f/∂x} + ∂/∂y{(y^2)*∂f/∂y} = 0

 

[haruspex]

The powers "-1/2" in the very first step for both f_x and f_y should be "+1/2".

 

[aruwin]

The powers "-1/2" in the very first step for both f_x and f_y should be "+1/2".

I think my first partial derivative is correct.

because the power of the original function is +1/2 so when we differentiate it,it becomes
1/2 - 1 = -1/2

But I don't get 0 for the final answer

 

[haruspex]

Sorry, you're right. The mistakes are in the last line.
In fact, hardly any of the last line looks right to me!
E.g. the first term should be (writing g = 1/f):
[-2xyg³ + 3y²(1-x²)g]/g⁶
No?

 

[aruwin]

Sorry, you're right. The mistakes are in the last line.
In fact, hardly any of the last line looks right to me!
E.g. the first term should be (writing g = 1/f):
[-2xyg³ + 3y²(1-x²)g]/g⁶
No?

Yeah, I know what went wrong now :D I used the quotient rule incorrectly.
Thanks, I have solved this! :)