Second Derivatives - Help.

Questions
,
1

Hello,

I bought the app you for AppStore, I am a customer from Brazil.
I could not solve second derivative questions, could you help me?

I would like to find the derivatives of a function in shapes: X, Y, XX, XY, YX, YY.

Example:
F (X, Y) = e ^ (2-x) / Y ^ 2

F (x) =
F (y) =
F (xx) =
F (xy) =
F (yx) =
F (yy) =

Can you explain me how to write these formulas in the application?

Thanks !!

2

Hi,

I do not really understand your question and I do not know what application you are talking about. If you define

F[x, y] := Exp[2 - x]/y^2

these lines generate the derivatives that your are looking for:

D[F[x, y], #] & /@ {x, y}

and

D[F[x, y], #[[1]], #[[2]]] & /@ Tuples[{x, y}, 2]

There are probably easier ways. If you want to set all of them equal as you appear to suggest in your post you can use:

Equal @@ Union[D[F[x, y], #] & /@ {x, y}, D[F[x, y], #[[1]], #[[2]]] & /@ Tuples[{x, y}, 2]]

Cheers,

Marco

PS: You might also want to use the proper formatting when you post. If you put the formulas in the appropriate code boxes it is easier to reply. Also I am not sure whether the use of capital Y and small y is intentional or just a typo.

PPS: I also might be answering something completely wrong, because I do not know what App from the AppStore you are talking about. Is is the Wolfram alpha app?

3

Hello,

and easy extension would be

In[31]:= f[x_, y_] := e^(2 - x)/y^2
Table[Derivative[i, j][f][x, y], {i, 0, 2}, {j, 0, 2}]

Out[32]= {{e^(2 - x)/y^2, -((2 e^(2 - x))/y^3), (6 e^(2 - x))/
  y^4}, {-((e^(2 - x) Log[e])/y^2), (2 e^(2 - x) Log[e])/
  y^3, -((6 e^(2 - x) Log[e])/y^4)}, {(e^(2 - x) Log[e]^2)/
  y^2, -((2 e^(2 - x) Log[e]^2)/y^3), (6 e^(2 - x) Log[e]^2)/y^4}}