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<A NAME=TANH>

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



<B>TANH</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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The <em>tanh</em> operator returns the hyperbolic tangent of its argument. 
The derivative of <em>tanh</em> and some simple transformations are known 
to the system. 
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 <P> <H3> 
syntax: </H3>
<em>tanh</em>(&lt;expression&gt;) or <em>tanh</em> &lt;simple\_expression&gt; 
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&lt;expression&gt; may be any scalar REDUCE expression, not an array, matrix or 

vector expression. &lt;simple\_expression&gt; must be a single identifier or 
begin with a prefix operator name. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
tanh b; 

  TANH(B) 


tanh(0); 

  0 


df(tanh(x*y),x); 

                 2
  Y*( - TANH(X*Y)  + 1) 


int(tanh(x),x); 

       2*X
  LOG(E    + 1) - X 


on rounded; tanh 2; 

  0.964027580076

</TT></PRE><P>You may attach further functionality by defining its inverse (see 


<A HREF=r37_0247.html>atanh</A>). 
A numeric value is not returned by <em>tanh</em> unless the switch 

<A HREF=r37_0330.html>rounded</A> is on and its argument evaluates to a number. 

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