How to Set a Variable Equal to a Constant with Zero Derivative in Mathematica?

[codemonkey209]

Hello everyone,
I just started using Mathematica and was wondering how do you set a variable, such as 'A' or 'B', equal to a constant whose derivative is equal to zero. So for example if I were to input something like this:

Dt[A*E^(2 x)*Cos[3 x] + B*E^(2x)*Sin[3 x], {x, 2}]

it wouldn't include something like this in the answer:

Dt[B, x]

but instead take it to be zero thus simplifying the outputted answer.

 

[shoehorn]

Unless you specify that a variable is a constant, Mathematica will assume that it has a non-zero total derivative. For instance, if you want to compute the total derivative with respect to x of the function a*x^n, a naive application of the Dt method gives you the following:

 In[1]:= Dt[a*x^n, x]
Out[1]:= x^n Dt[a, x] + a x^n (n/x + Dt[n, x] Log[x])

This is perfectly correct since it represents a general application of the Leibniz rule for derivatives. However, if you know that a and n are independent of x, there's clearly more information in the answer than is necessary. Hence, you might specify that a and n are constants as follows:

 In[2]:= Dt[a*x^n, x, Constants->{a, n}]
Out[2]:= a n x^(-1 + n)

This is all mentioned in the first paragraph of the Mathematica documentation for Dt, by the way.

 

[Hepth]

Or you can just use "D" instead of "Dt" unless you WANT the full derivatives for some things but not others?

 

[shoehorn]

Or you can just use "D" instead of "Dt" unless you WANT the full derivatives for some things but not others?

Well, yes; in fact my first thought was to point out that pretty much the same thing could be achieved by computing the partial derivative. However, I assume that there's some particular significance to the fact that he/she has gone to the trouble of using Dt[] to compute the total derivative.

 

[blue_raver22]

I understand the importance of using efficient and accurate computational tools in our work. Mathematica is a powerful software that allows us to perform complex mathematical calculations and analyze data quickly and accurately. In response to your question, setting a variable equal to a constant whose derivative is zero is a common practice in mathematical and scientific calculations. In Mathematica, you can achieve this by using the "Set" function, denoted by the equal sign (=). For example, if you want to set A equal to a constant c, you would write "A=c" in the input line. This will ensure that the derivative of A is zero in any subsequent calculations.

In your specific example, you can use the "Simplify" function to simplify the output by telling Mathematica to assume that B is a constant. You can do this by adding the assumption "Assuming[B \[Element] Reals, Simplify[Dt[A*E^(2x)*Cos[3x]+B*E^(2x)*Sin[3x], {x, 2}]]" to your input line. This will result in the output you desire without including the term Dt[B, x].

I hope this helps you in your exploration of Mathematica and its capabilities. Remember to always double check your inputs and assumptions to ensure accurate results. Happy computing!