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<A NAME=DF>

<TITLE>DF</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>DF</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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The <em>df</em> operator finds partial derivatives with respect to one or 
more variables. 
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 <P> <H3> 
syntax: </H3>
<em>df</em>(&lt;expression&gt;<em>,</em>&lt;var&gt; 
	 [<em>,</em>&lt;number&gt;] 
 {<em>,</em>&lt;var&gt; [ <em>,</em>&lt;number&gt;] } ) 
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&lt;expression&gt; can be any valid REDUCE algebraic expression. &lt;var&gt; 
must be a 
<A HREF=r37_0002.html>kernel</A>, and is the differentiation variable. 
&lt;number&gt; must be a non-negative integer. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>

df(x**2,x); 

  2*X 



df(x**2*y + sin(y),y); 

            2
  COS(Y) + X  



df((x+y)**10,z); 

  0 




df(1/x**2,x,2); 

  6
  ---
   4
  X



df(x**4*y + sin(y),y,x,3); 

  24*X 



for all x let df(tan(x),x) = sec(x)**2; 


df(tan(3*x),x); 

            2
  3*SEC(3*X)

</TT></PRE><P>An error message results if a non-kernel is entered as a different
iation 
operator. If the optional number is omitted, it is assumed to be 1. 
See the declaration 
<A HREF=r37_0192.html>depend</A> to establish dependencies for implicit 
differentiation. 
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You can define your own differentiation rules, expanding REDUCE's 
capabilities, using the 
<A HREF=r37_0199.html>let</A> command as shown in the last example 
above. Note that once you add your own rule for differentiating a 
function, it supersedes REDUCE's normal handling of that function for the 
duration of the REDUCE session. If you clear the rule 
(
<A HREF=r37_0190.html>clearrules</A>), you don't get back 
to the previous rule. 
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