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Have a complex calculus problem involving analytic expressions

GROUPS:
This involves integration, partial and ordinary derivatives of analytical expressions.

Do we have a tool that I can use to check my work?

Example: I want to take the fifth derivative of SIN(x)*cos(y) and all partial derivatives, wrt
to X and Y. I want to make sure I did it correctly.

Then I want to evaluate the results between limits also given by algebraic expressions.

Another example; I have three complex analytic expressions in three variables X, Y and Z,
and I want an analytic solution to X, Y and Z if one exists.
POSTED BY: William Sinclair
Answer
5 months ago
I hope this is similar to what you wish to see. 
 Clear["Global`*"];
 
 (* Part 1 *)
 f[x_, y_] := Sin[x] Cos[y];          (* Specify the function *)
 D[ f[x,y], x]                        (* Differentiate w.r.t any number of variables *)
 Evaluate[ % /. {y -> 0.5, x -> 0.4}] (* Evaluate the answer for specified value of variable *)
 
 (* Part 2 *)
 (* Enter three equations in 3-variables and solve. *)
Solve[ {2x - y + z == 1, y + z == 0, x + y + z == 0}, {x, y, z}]
POSTED BY: Isaac Abraham
Answer
5 months ago
Hi Isaac;

What package is that from? Is that a special interactive language?
I don't recognize this one.

Anyway, I want to take HIGHER order derivatives, which means some sort of recursion
would be part of the process.

The numerical part isn't important, but the ANALYTICAL part needs to be checked.
POSTED BY: William Sinclair
Answer
5 months ago
That's the output of standard Mathematica. In Mathematica, one could use the following syntax for higher order derivatives.
D[ f[x,y], {x, n}]
...where n is the nth derivative of  f[x, y].
POSTED BY: Isaac Abraham
Answer
5 months ago