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Cornel19-Tanzanite
19-Tanzanite
June 30, 2022
Solved

Calculation of Derivatives - Create Mathcad Program/Function

  • June 30, 2022
  • 2 replies
  • 1578 views

Hello,

I would like to get a program in Mathcad that: given being a function with a certain number of parameters and a certain symbolic expression, f (p1, p2, p3, p4, ..., pn): = a certain symbolic expression that involves these parameters: p1, p2, p3, ... ,pn, to automatically obtain the following:

1.  Symbolic calculation of:

CornelBejan_1-1656590551502.png

 

2. Numerical calculation of:

Given finally the numerical values ​​for the parameters: p1, p2, p3, ..., pn, calculate the numerical values ​​for the expressions of the derivatives from point 1.

Example for the case with 3 variables: p1, p2, p3:

CornelBejan_3-1656590786428.png

 

1. Symbolic calculation:

CornelBejan_4-1656590804089.png

 

2. Numerical calculation

CornelBejan_5-1656590822354.png

 

The idea is that I want a Mathcad program that calculates automatically what I want regarding the two points above (point 1 and point 2), meaning to give me as output both the symbolic calculations and the numerical calculations, in the form of parameters, as shown for example in the example above (Sp1, Sp2, Sp3, Sp4, Sp5, Sp6), and not me each time to calculate in turn them one by one, line by line.

 

Attached is the Mathcad file in Mathcad 15, Mathcad 11 and Mathcad Prime 7.0.0 versions.

 

Best answer by Werner_E

You could define a vector function and use the gradient/Nabla operator:

Werner_E_0-1656619113824.png

Of course you could also turn your existing function in a three separate arguments into a vector function

Werner_E_0-1656671363717.png

But I guess it would not hard to write a function which can deal with input functions with a variable number of arguments. Even if you provide that number as a separate argument to your function.

 

2 replies

W
Werner_E25-Diamond IAnswer
25-Diamond I
June 30, 2022

You could define a vector function and use the gradient/Nabla operator:

Werner_E_0-1656619113824.png

Of course you could also turn your existing function in a three separate arguments into a vector function

Werner_E_0-1656671363717.png

But I guess it would not hard to write a function which can deal with input functions with a variable number of arguments. Even if you provide that number as a separate argument to your function.

 

    L
    LucMeekes23-Emerald IV
    23-Emerald IV
    July 7, 2022

    You can define such a function as follows (in Mathcad 11, may work in Mathcad 15, will NOT work in Prime):

    LucMeekes_0-1657228936519.png

    Your example:

    LucMeekes_1-1657228981872.png

    Another example:

    LucMeekes_2-1657229013162.png

    Success!
    Luc

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