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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: FDIFF_3:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">x0</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">f1</font> <a href="fdiff_3.html#R3" title="FDIFF_3:pred.3">is_right_differentiable_in</a> <font color="Olive" title="b3">x0</font> &amp; <font color="Olive" title="b2">f2</font> <a href="fdiff_3.html#R3" title="FDIFF_3:pred.3">is_right_differentiable_in</a> <font color="Olive" title="b3">x0</font> holds <br/>( <font color="Olive" title="b1">f1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b2">f2</font> <a href="fdiff_3.html#R3" title="FDIFF_3:pred.3">is_right_differentiable_in</a> <font color="Olive" title="b3">x0</font> &amp;  <a href="fdiff_3.html#K2" title="FDIFF_3:func.2">Rdiff</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b2">f2</font></span>)</span>,<font color="Olive" title="b3">x0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_3.html#K2" title="FDIFF_3:func.2">Rdiff</a> (<font color="Olive" title="b1">f1</font>,<font color="Olive" title="b3">x0</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x0</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_3.html#K2" title="FDIFF_3:func.2">Rdiff</a> (<font color="Olive" title="b2">f2</font>,<font color="Olive" title="b3">x0</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x0</font></span>)</span></span>)</span> )</div></div>
