Wolfram Language

Symbolic & Numeric Calculus

Generate a Gallery of Difference Quotients

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

In[1]:=
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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.

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In[2]:=
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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=

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