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<b>let </b><font color="Maroon" title="c1">p</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<a NAME="E1:66"/>
(  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  is  <a href="rcomp_1.html#V3" title="RCOMP_1:attr.3">open</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp; ( for <font color="Olive" title="b1">p</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds <br/> <a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="fdiff_1.html#R1" title="FDIFF_1:pred.1">is_differentiable_in</a> <font color="Olive" title="b1">p</font> ) )
 
<b>by </b><i><a class="txt" href="sin_cos2.html#E61"><i><font color="Green" title="E40">Lm23</font></i></a>, <a class="txt" href="sin_cos2.html#E62"><i><font color="Green" title="E41">Lm24</font></i></a>, <a class="ref" href="fcont_3.html#T4" title="FCONT_3:th.4">FCONT_3:4</a></i>;<br/>
<b>hence </b><a NAME="E2:66"/>
(  <a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a>  <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp;  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <a href="sin_cos2.html#K7" title="SIN_COS2:func.7">tanh</a> ,<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K4" title="SIN_COS2:func.4">cosh</a>  <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="sin_cos2.html#E61"><i><font color="Green" title="E40">Lm23</font></i></a>, <a class="txt" href="sin_cos2.html#E62"><i><font color="Green" title="E41">Lm24</font></i></a>, <a class="ref" href="sin_cos2.html#T30" target="_self" title="SIN_COS2:th.30">Th30</a>, <a class="ref" href="fdiff_1.html#T16" title="FDIFF_1:th.16">FDIFF_1:16</a></i>;<br/>


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