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# What is the difference between variable "t" and variable "y" ?

Posted 10 years ago
 I am trying to define a function of variables "x" and "t" and take partial derivatives with respect to each. The function is as follows: f[x_,t_]=Cos[x-t]  When defining the function using variable "t" the output becomes: Cos[t-x]  Then taking the partial derivative w.r.t "t" using D[f,t] returns 0 (zero). Substituting variable "y" for "t" returns a different (correct in my eyes) result. So my question is; What is the difference in the eyes of mathematica, to the variables "t" and "y" (or really any other variable that I could define)? I've posted screenshots to show exactly what my inputs were. Thank you so much in helping me better understand this. Attachments:
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Posted 10 years ago
 You can read up on some of the differences between = and := here:http://reference.wolfram.com/language/tutorial/ImmediateAndDelayedDefinitions.html
Posted 10 years ago
 Thank you, I thought I had tried that before moving on to using variable "y". I guess I didn't though as D[f[x,t],t] works just fine. My mistake.Why is using delayed evaluation advantageous over immediate evaluation?
Posted 10 years ago
 Look at your two examples carefully. In the first case you computed D[f,t] rather than D[f[x,t],t] By the way, you should define your functions using delayed evaluation (:=) rather than immediate evaluation (=)