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

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SUMMARY

The discussion centers on evaluating the mixed partial derivative (d^2)/(dxdy) of the function F = ax^2 + bxy + cy^2. Participants clarify that the correct approach involves applying the partial derivatives sequentially, specifically ∂(∂F/∂y)/∂x. The confusion arises from an initial attempt to multiply the derivatives instead of applying them in order, leading to an incorrect result. The correct answer is confirmed to be -b, aligning with the solution manual.

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

Is it just d/dx*d/dy?

Thanks!
 
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hi btbam91! :smile:
btbam91 said:
Is it just ∂/∂x*∂/∂y?

quick answer: yup! :biggrin:

(and it's also ∂/∂y*∂/∂x)
 
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!
 
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.
 
ohhh! :smile:

i assumed you meant ∂/∂x of ∂/∂y …

you ∂/∂y it first, then you ∂/∂x it …

∂(∂F/∂y)/∂x :wink:​
 
Oh! I got it now! Thanks fellas!
 

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