# Quick math question!

1. Mar 1, 2012

### btbam91

How do I evaluate (d^2)/(dxdy)?

Is it just d/dx*d/dy?

Thanks!

2. Mar 1, 2012

### tiny-tim

hi btbam91!

(and it's also ∂/∂y*∂/∂x)

3. Mar 1, 2012

### btbam91

Hmmm, double check my work because I must be doing something wrong!

I'm looking to evaluate -(d^2)/(dxdy) of F, where F = ax^2+bxy+cy^2

So for dF/dx, I get 2ax+by. For dF/dy, I get bx+2cy.

So, multiplying both together and accounting for the negative sign:

-[(2ax+by)*(bx+2cy)]= -[2abx^2+4acxy+b^2xy+2bcy^2]

The answer is supposed to be -b according to the solution manual (that doesn't show the solution :p)

Am I missing something here? Thanks!

4. Mar 1, 2012

### Integral

Staff Emeritus
Do not multiply, but apply each differential sequentially. So after finding the first differential, do the second on the resulting expression. Order is not critical.

5. Mar 1, 2012

### tiny-tim

ohhh!

i assumed you meant ∂/∂x of ∂/∂y …

you ∂/∂y it first, then you ∂/∂x it …

∂(∂F/∂y)/∂x

6. Mar 1, 2012

### btbam91

Oh! I got it now! Thanks fellas!