📄 ch11_3_1.htm
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<TITLE> 微分 </TITLE>
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<H1>11.3.1 微分</H1>
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<FONT COLOR=#FF0000 FACE="Times New Roman">diff</FONT>函数用以演算一函数的微分项，相关的函数语法有下列<FONT FACE="Times New Roman">4</FONT>个：
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<FONT COLOR=#FF0000 FACE="Times New Roman">diff(f) </FONT>传回<FONT COLOR=#FF0000 FACE="Times New Roman">f</FONT>对预设独立变数的一次微分值
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<FONT COLOR=#FF0000 FACE="Times New Roman">diff(f,</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">t</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">)</FONT><FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000> </FONT>传回<FONT COLOR=#FF0000 FACE="Times New Roman">f</FONT>对独立变数<FONT COLOR=#FF0000 FACE="Times New Roman">t</FONT>的一次微分值
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<FONT COLOR=#FF0000 FACE="Times New Roman">diff(f,n)</FONT><FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000> </FONT>传回<FONT COLOR=#FF0000 FACE="Times New Roman">f</FONT>对预设独立变数的<FONT COLOR=#FF0000 FACE="Times New Roman">n</FONT>次微分值
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<FONT COLOR=#FF0000 FACE="Times New Roman">diff(f,</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">t</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">,n)</FONT><FONT FACE="Times New Roman">
</FONT><FONT COLOR=#FF0000> </FONT>传回<FONT COLOR=#FF0000 FACE="Times New Roman">f</FONT>对独立变数<FONT COLOR=#FF0000 FACE="Times New Roman">t</FONT>的<FONT COLOR=#FF0000 FACE="Times New Roman">n</FONT>次微分值
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因为之前再第八章介绍的数值微分函数也是用<FONT COLOR=#FF0000 FACE="Times New Roman">diff</FONT>，因此这个函数是靠输入的引数决定是以数值或是符号
微分，如果引数为向量则执行数值微分，如果引数为符号表示式则执行符号微分。
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先定义下列三个方程式，接著再演算其微分项：
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>S1 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">6*x^3-4*x^2+b*x-5</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>S2 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">sin(a)</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>S3 = </FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">(1
- t^3)/(1 + t^4)</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">;
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>diff(S1)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">18*x^2-8*x+b</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>diff(S1,2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">36*x-8</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>diff(S1,</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">b</FONT><FONT COLOR=#FF0000>'</FONT><FONT COLOR=#FF0000 FACE="Times New Roman">)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">x</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>diff(S2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">cos(a)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>diff(S3)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">-3*t^2/(1+t^4)-4*(1-t^3)/(1+t^4)^2*t^3</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>simplify(diff(S3))</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">t^2*(-3+t^4-4*t)/(1+t^4)^2</FONT><HR>
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