Help with Derivatives in Mathcad

[czechman45]

I know that Mathcad only takes partial derivatives. I set up my equations using this general format:

L:= x(t)

Then, I take the derivative of L with respect to t and get the following:

dL/dt -> d/dt*x(t)

However, when I take the derivative of L with respect to x, I should get 1, but am getting 0.

dL/dx -> 0

I've also tried typing dL/d(x(t)), but the program gets mad at me saying that I'm not using a name. Please help. I need Mathcad to take the derivatives of some big expressions with respect to both time and specific variables.

Thank you.

 

[I like Serena]

Hi czechman45, welcome to PF

I know that Mathcad only takes partial derivatives. I set up my equations using this general format:

L:= x(t)

Then, I take the derivative of L with respect to t and get the following:

dL/dt -> d/dt*x(t)

However, when I take the derivative of L with respect to x, I should get 1, but am getting 0.

dL/dx -> 0

I've also tried typing dL/d(x(t)), but the program gets mad at me saying that I'm not using a name. Please help. I need Mathcad to take the derivatives of some big expressions with respect to both time and specific variables.

Thank you.

Since you have defined L without a parameter, as far as Mathcad knows, L is not dependent on any parameter, meaning it is treated as a constant.

To fix it you need to define:
L(t) := x(t)

This explains to Mathcad that L is a function with a parameter, and that x(t) is supposed to be used with this parameter.

 

[czechman45]

@I like Serena
I tried your suggestion. It works for dL/dt, but it still gives me 0 for dL/dx, where I'm supposed to be getting 1. Any other suggestions?

 

[I like Serena]

@I like Serena
I tried your suggestion. It works for dL/dt, but it still gives me 0 for dL/dx, where I'm supposed to be getting 1. Any other suggestions?

I'm guessing a bit, since I don't know what your large expressions look like.

I suspect you need L to be of the form:

L(t,x) := x

Now you can take d/dt from L(t,x(t)) and you can take d/dx from L(t,x).
The first derivative would be a total derivative, while the second is a partial derivative.

In particular each derivative you want to take requires L to have a parameter with the same name.

 

[alphy]

I understand your frustration with Mathcad's limitation in taking only partial derivatives. It is important to note that Mathcad is a computational software and its capabilities are limited by its programming. In this case, it seems that Mathcad is not recognizing the variable x as a function of t, hence the incorrect result of 0 for dL/dx.

One solution could be to explicitly define x as a function of t, such as x(t) := t^2. This way, Mathcad will recognize x as a function and be able to take the derivative correctly.

Another option would be to use a different software that allows for the calculation of partial derivatives, such as Mathematica or Maple. These programs have more advanced capabilities and may better suit your needs for taking derivatives of complex expressions with respect to multiple variables.

I hope this helps and good luck with your calculations. Remember, as a scientist, it is important to understand the limitations and capabilities of the tools we use and to find the best solution for our specific needs.