How to compute derivative of product with mupad?

Hi,

I was wondering how to compute the derivative of the product below in mupad. The expression below is in latex.

\[ L = \prod_{i=1}^{n}\frac{R_i}{1+R_i} \]

Thanks in advance!

Y-L

Answer 1

[Walter Roberson]

Is R_i indicating the i'th value of R, R(i) in MATLAB notation?

If so, then at the MuPad level, you would want

diff(product(R[i]/(1+R[i]), i = 1 .. n), V)

where V is the variable that you wish to differentiate with respect to.

If you are intending that your R[i] be expressions in a variable and you intend to differentiate with respect to that variable, then

simplify(diff(product(R[i](x)/(1+R[i](x)), i = 1 .. n), x))

Please note that the above is in MuPad language, not MATLAB directly. You would need to evalin(symengine,'....') or something similar to evaluate it at the MATLAB level.

[Yün Han]

I mean R_i is any value in the set R = {R_1,R_2,...,R_n}, and I want to compute the derivative of L with respect to R_i;

diff(product(R[i]/(1+R[i]), i = 1 .. n), R[i])

this command returns the sum of all derivatives of L w.r.t. R[i], i = 1..n, which is not what I want. Any further ideas?

Thanks.

Y-L

[Yün Han]

Oh, could you please give me some hint of how to compute 2nd order derivative of L w.r.t R[i]? Thanks.

[Walter Roberson]

Note that it is normal for the derivative of a product to be a sum.

Do you want to compute the partial derivative of L with respect to each of R[1], R[2], and so on??

That would be written as

diff(product(R[i]/(1+R[i]), i = 1 .. n), R[i] $ i = 1 .. n)

and the result simplifies to product(1/(1+R[i])^2, i=1..n)

[Walter Roberson]

In the diff() call, the second argument onwards are the variables to compute the partial derivative with respect to

diff(expression,x,y,x)

for example would calculate with respect to x first, then y, then x.

The $ notation above expands to the list R[1], R[2], ... R[n]