This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 D D[ f , x ] gives the partial derivative . D[ f , x , n ] gives the multiple derivative . D[ f , , , ... ] gives . D[ f , x ] can be input as . The character is entered as pd or \[PartialD]. The variable x is entered as a subscript. All quantities that do not explicitly depend on the are taken to have zero partial derivative. D[ f , , ... , NonConstants -> , ... ] specifies that the implicitly depend on the , so that they do not have zero partial derivative. The derivatives of built-in mathematical functions are evaluated when possible in terms of other built-in mathematical functions. Numerical approximations to derivatives can be found using N. D uses the chain rule to simplify derivatives of unknown functions. D[ f , x , y ] can be input as . The character \[InvisibleComma], entered as ,, can be used instead of an ordinary comma. It does not display, but is still interpreted just like a comma. See the Mathematica book: Section 1.5.2, Section 3.5.1. See also: Dt, Derivative. Related package: Calculus`VectorAnalysis`, NumericalMath`NLimit`. Further Examples Here is the derivative of with respect to x. In[1]:= Out[1]= Here is the familiar Chain Rule of first year calculus. In[2]:= Out[2]= This gives the fourth derivative of . In[3]:= Out[3]= Here is the partial derivative . In[4]:= Out[4]= Normally, if you differentiate a function with respect to x, say, Mathematica will treat all other parameters as constants. In[5]:= Out[5]= By specifying that t depends upon x, you can get the desired result for such expressions. In[6]:= Out[6]= Here are some advanced examples. In[7]:= Out[7]= In[8]:= Out[8]= Sometimes the derivative is kept unevaluated until an argument is substituted for which an evaluation can be given. In[9]:= Out[9]= In[10]:= Out[10]= In[11]:= Out[11]= In[12]:= Out[12]= In[13]:=