This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 3.5.3 Derivatives of Unknown Functions Differentiating a known function gives an explicit result. In[1]:= D[Log[x]^2, x] Out[1]= Differentiating an unknown function f gives a result in terms of f'. In[2]:= D[f[x]^2, x] Out[2]= Mathematica applies the chain rule for differentiation, and leaves the result in terms of f'. In[3]:= D[x f[x^2], x] Out[3]= Differentiating again gives a result in terms of f, f' and f''. In[4]:= D[%, x] Out[4]= When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated. In[5]:= D[g[x^2, y^2], x] Out[5]= This represents . Mathematica assumes that the order in which derivatives are taken with respect to different variables is irrelevant. In[6]:= D[g[x, y], x, x, y] Out[6]= You can find the value of the derivative when by replacing x with 0. In[7]:= % /. x->0 Out[7]= Output forms for derivatives of unknown functions.