This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 1.5.2 Differentiation Here is the derivative of with respect to . In[1]:= D[ x^n, x ] Out[1]= Mathematica knows the derivatives of all the standard mathematical functions. In[2]:= D[ ArcTan[x], x ] Out[2]= This differentiates three times with respect to x. In[3]:= D[ x^n, {x, 3} ] Out[3]= The function D[x^n,x] really gives a partial derivative, in which n is assumed not to depend on x. Mathematica has another function, called Dt, which finds total derivatives, in which all variables are assumed to be related. In mathematical notation, D[f,x] is like , while Dt[ f,x] is like . You can think of Dt as standing for "derivative total". Dt gives a total derivative, which assumes that n can depend on x. Dt[n,x] stands for . In[4]:= Dt[ x^n, x ] Out[4]= This gives the total differential . Dt[x] is the differential . In[5]:= Dt[ x^n ] Out[5]= Some differentiation functions. As well as treating variables like symbolically, you can also treat functions in Mathematica symbolically. Thus, for example, you can find formulas for derivatives of f[x], without specifying any explicit form for the function f. Mathematica does not know how to differentiate f, so it gives you back a symbolic result in terms of f'. In[6]:= D[ f[x], x ] Out[6]= Mathematica uses the chain rule to simplify derivatives. In[7]:= D[ 2 x f[x^2], x ] Out[7]=