📄 第二节 用mathematica求极限和求微分.htm
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lang=EN-US style="mso-font-kerning: 0pt"><font face="宋体" size="4">SetAttributes[c,Constant]<SPAN style="mso-spacerun: yes">
</SPAN>在各种情况下，定义c为常数</font></SPAN><font face="宋体" size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P>
</O:P></SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN
style="mso-font-kerning: 0pt"><font face="宋体" size="4">例<SPAN
lang=EN-US>2求下列函数的一阶导数</SPAN></font></SPAN><font face="宋体" size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P>
</O:P></SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN
style="mso-font-kerning: 0pt"><font face="宋体" size="4">（<SPAN lang=EN-US>1）y=<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1065
style="HEIGHT: 15.75pt; WIDTH: 84pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
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<SPAN style="mso-spacerun: yes"> </SPAN>（2）y=<SPAN
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style="HEIGHT: 14.25pt; WIDTH: 38.25pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image074.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm57.gif"
v:shapes="_x0000_i1066" width="51" height="19"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1066"
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</SPAN></font></SPAN><font face="宋体" size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P></O:P></SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font face="宋体" size="4">(3)<SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1067
style="HEIGHT: 18pt; WIDTH: 90.75pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
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v:shapes="_x0000_i1067" width="121" height="24"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1067"
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<SPAN style="mso-spacerun: yes">
</SPAN>(4)y=<SPAN style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE
id=_x0000_i1068 style="HEIGHT: 18pt; WIDTH: 38.25pt" o:ole=""
type="#_x0000_t75"> <V:IMAGEDATA o:title=""
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</font>
</SPAN><font face="宋体" size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P></O:P></SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font face="宋体" size="4">解：</font></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">（</font><SPAN
lang=EN-US><font face="Times New Roman" size="4">1</font><font size="4">）</font><font face="Times New Roman" size="4">In[15]:=D[2x^3 + 5x^2 + Sin[7], x]<O:P> </font></SPAN></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4"> </font></SPAN><font face="Times New Roman"><SPAN
lang=EN-US style="mso-font-kerning: 0pt"><font size="4">Out[15]=<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1069
style="HEIGHT: 15.75pt; WIDTH: 48.75pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image080.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm60.gif"
v:shapes="_x0000_i1069" width="65" height="21"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1069"
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</font>
</SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">（</font><SPAN
lang=EN-US><font face="Times New Roman" size="4">2</font><font size="4">）</font><font face="Times New Roman" size="4">In[16]:=D[Log[Cos[x]], x]<O:P> </font></SPAN></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4"> </font></SPAN></b><b><font face="Times New Roman"><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4">Out[16]=-Tan[x]</font></SPAN><font size="4"><SPAN
lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P>
</SPAN></font></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">（</font><SPAN lang=EN-US><font face="Times New Roman" size="4">3</font><font size="4">）</font><font face="Times New Roman" size="4">In[17]:=D[E^y
+ x*y - E == Sin[y], x, NonConstants -> {y}]<O:P> </font></SPAN></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4"> </font></SPAN></b><b><font face="Times New Roman"><SPAN
lang=EN-US style="mso-font-kerning: 0pt"><font size="4">Out[17]=y+<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1070
style="HEIGHT: 15.75pt; WIDTH: 14.25pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image082.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm61.gif"
v:shapes="_x0000_i1070" width="19" height="21"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1070"
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D[y, x, NonConstants -> {y}] +x D[y, x, NonConstants -> {y}] ==Cos[y] D[y,
x, NonConstants -> {y}]</font></SPAN><font size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P>
</SPAN></font></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">（</font><SPAN lang=EN-US><font face="Times New Roman" size="4">4</font><font size="4">）</font><font face="Times New Roman" size="4">In[18]:=D[y
== x^3 + y^3, x, NonConstants -> {y}]<O:P> </font></SPAN></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4"> </font></SPAN></b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><b><font face="Times New Roman" size="4">Out[18]=(D[y, x, NonConstants
-> {y}] ==<SPAN style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE
id=_x0000_i1071 style="HEIGHT: 18pt; WIDTH: 50.25pt" o:ole=""
type="#_x0000_t75"> <V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image084.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm62.gif"
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D[y, x, NonConstants -> {y}]<O:P> </O:P></font></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN
style="mso-font-kerning: 0pt"><font size="4">例<SPAN
lang=EN-US><font face="Times New Roman">3</font>求下列函数的三阶导数</SPAN></font></SPAN><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><font size="4"><O:P>
</O:P></font></SPAN></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN
style="mso-font-kerning: 0pt"><font size="4">（</font><SPAN lang=EN-US><font face="Times New Roman" size="4">1</font><font size="4">）</font><font face="Times New Roman" size="4">y=ln cos
x<SPAN style="mso-spacerun: yes"> </SPAN></font><font size="4">（</font><font face="Times New Roman" size="4">2</font><font size="4">）</font><font face="Times New Roman" size="4">y=<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1072
style="HEIGHT: 15.75pt; WIDTH: 14.25pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image086.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm63.gif"
v:shapes="_x0000_i1072" width="19" height="21"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1072"
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</font>
</SPAN></SPAN><font face="Times New Roman"><font size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P></O:P></SPAN></font></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">解：</font></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">（</font><SPAN
lang=EN-US><font face="Times New Roman" size="4">1</font><font size="4">）</font><font face="Times New Roman" size="4">In[19]:=D[Log[Cos[x]], {x, 3}]<O:P> </O:P></font></SPAN></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><font face="Times New Roman"><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4">
Out[19]=<SPAN
style="mso-text-raise: -5.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1073
style="HEIGHT: 18pt; WIDTH: 87pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image088.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm64.gif"
v:shapes="_x0000_i1073" width="116" height="24"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1073"
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</font>
</SPAN><font size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><O:P></O:P></SPAN></font></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
style="mso-font-kerning: 0pt"><b><font size="4">（</font><SPAN
lang=EN-US><font face="Times New Roman" size="4">2</font><font size="4">）</font><font face="Times New Roman" size="4">In[20]:=D[x^7, {x, 3}]<O:P> </O:P></font></SPAN></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><font face="Times New Roman"><b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4">
</font>
</SPAN></b><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font size="4"><b>Out[20]=<SPAN
style="mso-text-raise: -3.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1074
style="HEIGHT: 15.75pt; WIDTH: 33pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
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src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image090.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm65.gif"
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