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

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Discussion Overview

The discussion revolves around the evaluation of the mixed partial derivative (d^2)/(dxdy), with a focus on its application in calculus. Participants explore the correct method for computing this derivative, particularly in the context of a specific function.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant asks how to evaluate (d^2)/(dxdy), questioning if it is simply d/dx*d/dy.
  • Another participant suggests that it is indeed ∂/∂x*∂/∂y and notes that the order can be reversed.
  • A participant presents a specific function F = ax^2 + bxy + cy^2 and attempts to compute the mixed partial derivative, expressing confusion over the expected result.
  • Another participant advises against multiplying the derivatives and suggests applying each differential sequentially instead.
  • One participant clarifies the correct order of differentiation, indicating that the derivative with respect to y should be taken first, followed by x.

Areas of Agreement / Disagreement

There is no consensus on the method of evaluation, as participants express differing approaches to computing the mixed partial derivative and the correct sequence of operations.

Contextual Notes

Some participants may be missing assumptions regarding the application of derivatives, and there is uncertainty about the expected outcome of the evaluation.

Who May Find This Useful

Students and individuals interested in calculus, particularly those working with partial derivatives and their applications in mathematical functions.

btbam91
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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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