I have been trying to use Wolfram|Alpha to get the partial derivatives of this function:
derivatives of Abs[(Sum (a + b*I) * exp(I*2*π*t*n*(x + ((n+1)/2)*y*t)), n=1 to k)]
But no success. Wolfram can't understand the query. Any ideas?
I think I was able to get W|A to understand the query
D[(Abs(Sum (a + b*I) * exp(I*2*π*t*n*(x + ((n+1)/2)*y*t)), n=1 to k)),t]
Link to WA Page
and substituting x or y for that last t seemed to work similarly.
All those derivatives resulted in zero and I would check that result before depending on it
Oddly, after completing this post and returning to the W|A page again and running the same calculation again took much longer with the display jiggling and it ended with the "didn't understand" page. I've seen that now and then in the past and have not been able to track down exactly what causes this. Fortunately, this time, closing the browser completely and starting over with that W|A input was sufficient for it to again report that the derivative was zero.