This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 Derivative f ' represents the derivative of a function f of one argument. Derivative[ , , ... ][ f ] is the general form, representing a function obtained from f by differentiating times with respect to the first argument, times with respect to the second argument, and so on. f ' is equivalent to Derivative[1][ f ]. f '' evaluates to Derivative[2][ f ]. You can think of Derivative as a functional operator which acts on functions to give derivative functions. Derivative is generated when you apply D to functions whose derivatives Mathematica does not know. Mathematica attempts to convert Derivative[ n ][ f ] and so on to pure functions. Whenever Derivative[ n ][ f ] is generated, Mathematica rewrites it as D[ f [#]&, #, n ]. If Mathematica finds an explicit value for this derivative, it returns this value. Otherwise, it returns the original Derivative form. Example: Cos'. Derivative[ , , ... ][ f ] represents the derivative of f [ , , ... ] taken times with respect to . In general, arguments given in lists in f can be handled by using a corresponding list structure in Derivative. N[ f '[ x ]] will give a numerical approximation to a derivative. See the Mathematica book: Section 2.2.8, Section 3.5.4. See also: D, Dt. Further Examples Here is the first derivative of the sine function given as a pure function. In[1]:= Out[1]= This gives the more familiar functional form. In[2]:= Out[2]= Here is a function of two variables. In[3]:= This gives the partial derivative with respect to the first variable once and with respect to the second variable three times. In[4]:= Out[4]=