# DerivativeFilter and List Manipulation

I have a list with about 8000 pairs of values like

      List ={{0,1},{1.2,4},{1.6,8},{2.11111,10},...}


and I want to have a list with the derivate of the function using DerivativeFilter[ ] upon the entries. To do so, i want to extract just the second value of the list, i.e. obtain

        List2= {1,4,8,10,....}


I didnt find any solution to my problem to do that easily.

Also: Is there an easier way to gain the derivate? And another question: How could I act with an operation only on the first or second variable of the pair, for example

          List3={{0,f[1]},{1.f[2,4]},{1.6,f[8]},{2.11111,f[10]},...}


Thanks for the help!

• List is a built-in command - don't use it as a name for user-defined variables! All MMA built-in commands are upper case (there's also N and D and many more). It's safest to always use lower case user-defined names. – corey979 Feb 22 '18 at 19:19

list1 = {{0, 1}, {1.2, 4}, {1.6, 8}, {2.11111, 10}};
list2 = list1[[All, 2]]


{1, 4, 8, 10}

list3 = MapAt[f, list1, {{All, -1}}]


{{0, f[1]}, {1.2, f[4]}, {1.6, f[8]}, {2.11111, f[10]}}

Also

list2b = Last /@ list1


{1, 4, 8, 10}

list3b = list1; list3b[[All, -1]] = f /@ list3b[[All, -1]]; list3b


{{0, f[1]}, {1.2, f[4]}, {1.6, f[8]}, {2.11111, f[10]}}