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<A NAME=ASINH>

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



<B>ASINH</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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The <em>asinh</em> operator returns the hyperbolic arcsine of its argument. 
The derivative of <em>asinh</em> and some simple transformations are known 
to the system. 
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 <P> <H3> 
syntax: </H3>
<em>asinh</em>(&lt;expression&gt;) or <em>asinh</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>
asinh d; 

  ASINH(D) 


asinh(1); 

  ASINH(1) 


df(asinh(2*x),x); 

            2
  2*SQRT(4*X  + 1))
  ----------------- 
         2
      4*X  + 1

</TT></PRE><P>You may attach further functionality by defining <em>asinh</em> to
 be the 
inverse of <em>sinh</em>. This is done by the commands 
<P><PRE><TT>
        put('sinh,'inverse,'asinh);
        put('asinh,'inverse,'sinh);
</TT></PRE><P><P>
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A numeric value is not returned by <em>asinh</em> unless the switch 
<em>rounded</em> is on and its argument evaluates to a number. 
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