second partial derivatives

[anjanesh]

I asked chatgpt one question about second partial derivatives.

$$f(x,y)=3x 2 −2xy+y^2 −8y.$$
But how did it come up with this as second partial derivatives ?

$$f xx = ∂^2 f/∂x^2 =6$$$$f yy = ∂^2 f/∂y^2 =2$$$$f xy = ∂^2 f/∂x∂y =−2$$

 

[mmm4444bot]

how did it come up with this as second partial derivatives ?

Why not ask it?
$\;$

 

[mario99]

I asked chatgpt one question about second partial derivatives.

$$f(x,y)=3x 2 −2xy+y 2 −8y.$$
But how did it come up with this as second partial derivatives ?

$$f xx = ∂^2 f/∂x^2 =6$$$$f yy = ∂^2 f/∂y^2 =2$$$$f xy = ∂^2 f/∂x∂y =−2$$

The second partial derivatives are correct. For example, $f_{xx}$ means take derivative with respect to $x$ twice.

 

[anjanesh]

means take derivative with respect to x twice.

Ah...thanks.

 

[anjanesh]

Why not ask it?
$\;$

I was afraid of it giving incorrect answers.

 

[Steven G]

I was afraid of it giving incorrect answers.

But you did ask it.

 

[Dr.Peterson]

I was afraid of it giving incorrect answers.

But of course that's why you should ask not just for the answers (which may well be wrong), but for the reasons (which you can then check).

This is how you should interact with any fallible person; the reason tells you much more than the answer. In fact, this is why teachers don't just ask students for answers, but want to see their work ...