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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:66"/>
(  <a href="numbers.html#K1">REAL</a>  is  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  holds <br/> <a href="sin_cos2.html#K7" target="_self">tanh</a>  <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="txt" href="sin_cos2.html#E61"><i><font color="Green">Lemma40</font></i></a>, <a class="txt" href="sin_cos2.html#E62"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="fcont_3.html#T4">FCONT_3:4</a>, <a class="ref" href="subset_1.html#D4">SUBSET_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E2:66"/>
(  <a href="sin_cos2.html#K7" target="_self">tanh</a>  <a href="fdiff_1.html#R2">is_differentiable_on</a>  <a href="numbers.html#K1">REAL</a>  &amp;  <a href="fdiff_1.html#K1">diff</a> <a href="sin_cos2.html#K7" target="_self">tanh</a> ,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos2.html#K4" target="_self">cosh</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="sin_cos2.html#E61"><i><font color="Green">Lemma40</font></i></a>, <a class="txt" href="sin_cos2.html#E62"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="sin_cos2.html#T30" target="_self">Th30</a>, <a class="ref" href="fdiff_1.html#T16">FDIFF_1:16</a></i>;<br/>


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