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<title> 微分 </title>
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<font COLOR="#0000FF">
<h1>11.3.1 微分</h1>
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<p><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： </p>
<p><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 </p>
<p><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>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 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">diff(f,n)</font><font FACE="Times New Roman"> </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 </p>
<p><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>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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<p>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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<p>先定义下列三个方程式，接著再演算其微分项： </p>
<p><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> </p>
<p><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> </p>
<p><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">; <br>
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<p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S1)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">18*x^2-8*x+b</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S1,2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">36*x-8</font> </p>
<p><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> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">x</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">cos(a)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>diff(S3)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><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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<p><font COLOR="#FF0000" FACE="Times New Roman">>>simplify(diff(S3))</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">t^2*(-3+t^4-4*t)/(1+t^4)^2</font></p>
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