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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: PDIFF_4:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">p</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 3<br/>  for <font color="Olive" title="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 3</span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b3">f</font> <a href="pdiff_1.html#R3" title="PDIFF_1:pred.3">is_partial_differentiable_in</a> <font color="Olive" title="b2">p</font>,1 &amp; <font color="Olive" title="b3">f</font> <a href="pdiff_1.html#R3" title="PDIFF_1:pred.3">is_partial_differentiable_in</a> <font color="Olive" title="b2">p</font>,2 &amp; <font color="Olive" title="b3">f</font> <a href="pdiff_1.html#R3" title="PDIFF_1:pred.3">is_partial_differentiable_in</a> <font color="Olive" title="b2">p</font>,3 holds <br/> <a href="pdiff_4.html#K4" title="PDIFF_4:func.4">grad</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b3">f</font></span>)</span>,<font color="Olive" title="b2">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><a href="pdiff_4.html#K4" title="PDIFF_4:func.4">grad</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">p</font>)</span>)</span></div></div>
