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

• btbam91
In summary, the conversation is discussing how to evaluate the second partial derivative of a function F with respect to both x and y. The answer is found by taking the first partial derivative with respect to y, then taking the partial derivative of that result with respect to x. The order of the derivatives does not matter.
btbam91
How do I evaluate (d^2)/(dxdy)?

Is it just d/dx*d/dy?

Thanks!

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

(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!

i assumed you meant ∂/∂x of ∂/∂y …

you ∂/∂y it first, then you ∂/∂x it …

∂(∂F/∂y)/∂x

Oh! I got it now! Thanks fellas!

## 1. What does (d^2)/(dxdy) mean?

The notation (d^2)/(dxdy) is used to represent the second partial derivative of a multivariable function. It is the derivative of the derivative with respect to two different variables, x and y.

## 2. How do you evaluate (d^2)/(dxdy) for a specific function?

To evaluate (d^2)/(dxdy) for a specific function, you need to first find the first partial derivatives with respect to both x and y. Then, take the derivative of those derivatives with respect to the other variable. Finally, plug in the values for x and y to get the numerical answer.

## 3. What is the difference between (d^2)/(dxdy) and (d^2)/(dydx)?

There is no difference between (d^2)/(dxdy) and (d^2)/(dydx). They both represent the second partial derivative with respect to x and y, and the order in which the variables are written does not affect the result. This is known as Clairaut's theorem.

## 4. Can (d^2)/(dxdy) be negative?

Yes, (d^2)/(dxdy) can be negative. It depends on the values of the first partial derivatives and the specific function being evaluated. It is possible for both the first partial derivatives to be positive or negative, resulting in a positive or negative second partial derivative.

## 5. In what situations would (d^2)/(dxdy) be used?

(d^2)/(dxdy) is used in multivariable calculus to analyze the rate of change of a function with respect to two different variables. It is helpful in understanding how changes in one variable affect the other variable.

Replies
2
Views
1K
Replies
6
Views
3K
Replies
4
Views
2K
Replies
6
Views
3K
Replies
7
Views
2K
Replies
1
Views
2K
Replies
29
Views
2K
Replies
10
Views
1K
Replies
4
Views
1K
Replies
3
Views
2K