This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 3.5.5 Defining Derivatives You can define the derivative in Mathematica of a function f of one argument simply by an assignment like f'[x_]=fp[x]. This defines the derivative of to be . In this case, you could have used = instead of :=. In[1]:= f'[x_] := fp[x] The rule for f'[x_] is used to evaluate this derivative. In[2]:= D[f[x^2], x] Out[2]= Differentiating again gives derivatives of . In[3]:= D[%, x] Out[3]= This defines a value for the derivative of at the origin. In[4]:= g'[0] = g0 Out[4]= The value for g'[0] is used. In[5]:= D[g[x]^2, x] /. x->0 Out[5]= This defines the second derivative of g, with any argument. In[6]:= g''[x_] = gpp[x] Out[6]= The value defined for the second derivative is used. In[7]:= D[g[x]^2, {x, 2}] Out[7]= To define derivatives of functions with several arguments, you have to use the general representation of derivatives in Mathematica. Defining derivatives. This defines the second derivative of g with respect to its second argument. In[8]:= Derivative[0, 2][g][x_, y_] := g2p[x, y] This uses the definition just given. In[9]:= D[g[a^2, x^2], x, x] Out[9]=