Something like that should do it
function poly(variable, degree){
return degree*((variable)^(degree-1));
}
You shoud store your polynomial of degree n in an (n+1) 'array' and using Jquery each method
var result = 0;
$.each(array, function(index, value) {
result = result + poly(value,index);
});
Edit : if you don't know about jquery, you can use pure javascript for loop, for (var i = 0; i < myArray.length; i++) {...}