Differentiating a Sum in MATLAB

[sara_87]

Homework Statement

How do i differentiate a sum in MATLAB?

So for an example, if I have:
$$y = x^2 + \sum^{n}_{j=1}3x_{j}^4$$

I want to differentiate it with respect to x.
It should return: $$2x + \sum^{n}_{j=1}12x_{j}^3$$

Homework Equations

The Attempt at a Solution

If I want to differentiate y = x^3+2x, this is what i would do:
>> syms x
>> y = x^3+2*x
>> diff(y,x,1)

this gives:

ans =

3*x^2+2


which is correct but how would i do differentiation if i have a sum?

thank you.

 

[Päällikkö]

First of all, your problem is laid out wrong. If you differentiate x_i with respect to x, you ought to end up with 0, I think. If your sum consists of x's rather than x_i's, then sum x = Nx, and you needn't worry about the sums anymore.

I don't think the Matlab symbolic toolbox is too advanced, but I suppose you could "hack" it, e.g.:
z = sum(repmat(x, 1, 10));

Hope this answers your question.

 

[sara_87]

sorry, it should be:

$$y_n = x_n^2 + \sum^{n}_{j=1}3x_{j}^4+x_n^2$$

so the derivative is:

$$y' = 2x_n + \sum^{n}_{j=1}3x_{j}^4+2x_n$$

What does z = sum(repmat(x, 1, 10)); do?

thank you

 

[Päällikkö]

repmat just makes multiple instances of its input, e.g.
repmat(x, 1, 2) = [x, x]

I'm still a bit unclear as to what you're doing.
If you're differentiating y_n with respect to x_n, the sum reduces to 12x_n^3, i.e.
$$y_n' = 2x_n + 12x_n^3 + 2x_n$$

Do you then sum over the different y'_n or what? That way you'd get
$$y' = \sum_{i=1}^n y_i'= 2x_n + \sum_{i=1}^n 12x_i^3 + 2x_n$$

EDIT: This would be the same as taking the divergence, if I'm not mistaken.

 

[sara_87]

I want to defferentiate:

$$y_n = x_n^2 + \sum^{n}_{j=1}(3x_{j}^4+x_n^2)$$

with respect to x_n

I know that this should give:

$$2x_n + \sum^{n}_{j=1}(3x_{j}^4+2x_n)$$

but i want to try to get this result using matlab.