Generate a Gallery of Difference Quotients: New in Wolfram Language 11

Generate a Gallery of Difference Quotients

Compute the difference quotient of several functions and the related derivatives.

In[1]:=

fList = {1, x, x^2, x^3, x^4, 1/x, Sin[x], Cos[x], Sinh[x], Cosh[x], 
   a^(x)};
dqList = DifferenceQuotient[fList, {x, h}];
derList = Limit[dqList, h -> 0];

Display the results in a formatted table.

show complete Wolfram Language input

In[2]:=

Grid[Map[Style[#, ScriptLevel -> 0] &, 
   Prepend[Transpose[{fList, dqList, derList}], 
    Style[#, FontWeight -> Bold, FontSize -> Larger] & /@ {f[x], (
      f[x + h] - f[x])/h, f'[x]}], {2}], Dividers -> All, 
  Spacings -> {4, 2}, 
  Background -> {None, {{None, 
      LightBlue}}, {1, #} -> Hue[.6, .4, 1] & /@ Range[3]}, 
  BaseStyle -> {FontFamily -> Times, 
    FontSize -> 13}] // TraditionalForm

Out[2]//TraditionalForm=