Problem of summation-mathematica

[shafieza_garl]

MATHEMATICA:differentiate the summation

I need help.im having problem to differentiate my equation respect to the m_i;How can i differentiate the equation.
Second question is;When i set Y=2;how can i put the parameter like m_1;m_2;S_1;S_2;
what i just do is input it manually by changing m_1=m1;m_2=m2;
its very difficult if Y become larger number

Sum[(Subscript[\[Sigma], i] - Subscript[c, i])*(Subscript[q, i]/
          Subscript[T, i]), {i, 1, Y}] - 
   Sum[((1 - \[Beta])/(2 - \[Beta]))*(Subscript[d, i]*
      Subscript[q, i]) + 
       (1/2)*((Subscript[m, i] - 1)*Subscript[w, i]*Subscript[q, i]) + 
       (Subscript[A, i]/Subscript[m, i] + Subscript[S, i])/
         Subscript[T, i], {i, 1, Y}]

Thanx for da help

 

[Bill Simpson]

Y=2;
s=Sum[...];
d=D[s,Subscript[m,1]];
d/.Subscript[m,1]->4

 

[shafieza_garl]

Thanx a a lot for da help.but what is da function of

 d /. Subscript[m, 1] -> 4

and do you know how can input the subscript like m_1 and m_2 if they have value ?

 

[Bill Simpson]

expression/.variable->value
is an alternate way of writing the ReplaceAll function.
That function replaces all variable with value in expression.
Here is the documentation for ReplaceAll.
http://reference.wolfram.com/mathematica/ref/ReplaceAll.html
If you look at the value of the variable d in my code and compare that
with the value after the ReplaceAll you can see what it has done.

I am not certain I understand what you mean "if they have value."
If they have value then they are not a variable in your expression
and there is no variable to replace with a value.

 

[alphy]

The problem of summation in Mathematica can be solved by using the Sum function. To differentiate the equation with respect to m_i, you can use the D function and specify the variable as m_i.

For example, if your equation is written as f = Sum[m_i*x_i, {i, 1, Y}], then to differentiate it with respect to m_i, you can use the command D[f, m_i].

To set Y=2 and input the parameters m_1, m_2, S_1, S_2, you can use the Subscript function in Mathematica. For example, if you want to set m_1=m1, m_2=m2, S_1=S1, S_2=S2, you can write it as m_1 = Subscript[m, 1] = m1, m_2 = Subscript[m, 2] = m2, S_1 = Subscript[S, 1] = S1, S_2 = Subscript[S, 2] = S2.

It is important to note that when Y becomes a larger number, it is not practical to manually change the parameters. In this case, you can use loops or a list to input the parameters. For example, you can use a Table or Do loop to input the parameters for each value of Y.

Overall, Mathematica has many tools and functions that can help you solve problems with summations and differentiate equations. It is important to familiarize yourself with these functions and use them to efficiently solve your problems.