Quick Math Q: Evaluate (d^2)/(dxdy) ?

[btbam91]

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

Is it just d/dx*d/dy?

Thanks!

 

[tiny-tim]

hi btbam91!

Is it just ∂/∂x*∂/∂y?

quick answer: yup!

(and it's also ∂/∂y*∂/∂x)

 

[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!

 

[Integral]

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.

 

[tiny-tim]

ohhh!

i assumed you meant ∂/∂x of ∂/∂y …

you ∂/∂y it first, then you ∂/∂x it …

∂(∂F/∂y)/∂x ​

 

[btbam91]

Oh! I got it now! Thanks fellas!