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<h3 class="section">27.4 Derivatives and Integrals</h3>
<p>Octave comes with functions for computing the derivative and the integral
of a polynomial. The functions <code>polyderiv</code> and <code>polyint</code>
both return new polynomials describing the result. As an example we'll
compute the definite integral of p(x) = x^2 + 1 from 0 to 3.
<pre class="example"> c = [1, 0, 1];
integral = polyint(c);
area = polyval(integral, 3) - polyval(integral, 0)
12
</pre>
<!-- ./polynomial/polyderiv.m -->
<p><a name="doc_002dpolyderiv"></a>
<div class="defun">
— Function File: <b>polyderiv</b> (<var>c</var>)<var><a name="index-polyderiv-2040"></a></var><br>
— Function File: [<var>q</var>] = <b>polyderiv</b> (<var>b, a</var>)<var><a name="index-polyderiv-2041"></a></var><br>
— Function File: [<var>q</var>, <var>r</var>] = <b>polyderiv</b> (<var>b, a</var>)<var><a name="index-polyderiv-2042"></a></var><br>
<blockquote><p>Return the coefficients of the derivative of the polynomial whose
coefficients are given by vector <var>c</var>. If a pair of polynomials
is given <var>b</var> and <var>a</var>, the derivative of the product is
returned in <var>q</var>, or the quotient numerator in <var>q</var> and the
quotient denominator in <var>r</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpoly.html#doc_002dpoly">poly</a>, <a href="doc_002dpolyinteg.html#doc_002dpolyinteg">polyinteg</a>, <a href="doc_002dpolyreduce.html#doc_002dpolyreduce">polyreduce</a>, <a href="doc_002droots.html#doc_002droots">roots</a>, <a href="doc_002dconv.html#doc_002dconv">conv</a>, <a href="doc_002ddeconv.html#doc_002ddeconv">deconv</a>, <a href="doc_002dresidue.html#doc_002dresidue">residue</a>, <a href="doc_002dfilter.html#doc_002dfilter">filter</a>, <a href="doc_002dpolygcd.html#doc_002dpolygcd">polygcd</a>, <a href="doc_002dpolyval.html#doc_002dpolyval">polyval</a>, <a href="doc_002dpolyvalm.html#doc_002dpolyvalm">polyvalm</a>.
</p></blockquote></div>
<!-- ./polynomial/polyder.m -->
<p><a name="doc_002dpolyder"></a>
<div class="defun">
— Function File: <b>polyder</b> (<var>c</var>)<var><a name="index-polyder-2043"></a></var><br>
— Function File: [<var>q</var>] = <b>polyder</b> (<var>b, a</var>)<var><a name="index-polyder-2044"></a></var><br>
— Function File: [<var>q</var>, <var>r</var>] = <b>polyder</b> (<var>b, a</var>)<var><a name="index-polyder-2045"></a></var><br>
<blockquote><p>See polyderiv.
</p></blockquote></div>
<!-- ./deprecated/polyinteg.m -->
<p><a name="doc_002dpolyinteg"></a>
<div class="defun">
— Function File: <b>polyinteg</b> (<var>c</var>)<var><a name="index-polyinteg-2046"></a></var><br>
<blockquote><p>Return the coefficients of the integral of the polynomial whose
coefficients are represented by the vector <var>c</var>.
<p>The constant of integration is set to zero.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpolyint.html#doc_002dpolyint">polyint</a>, <a href="doc_002dpoly.html#doc_002dpoly">poly</a>, <a href="doc_002dpolyderiv.html#doc_002dpolyderiv">polyderiv</a>, <a href="doc_002dpolyreduce.html#doc_002dpolyreduce">polyreduce</a>, <a href="doc_002droots.html#doc_002droots">roots</a>, <a href="doc_002dconv.html#doc_002dconv">conv</a>, <a href="doc_002ddeconv.html#doc_002ddeconv">deconv</a>, <a href="doc_002dresidue.html#doc_002dresidue">residue</a>, <a href="doc_002dfilter.html#doc_002dfilter">filter</a>, <a href="doc_002dpolyval.html#doc_002dpolyval">polyval</a>, <a href="doc_002dpolyvalm.html#doc_002dpolyvalm">polyvalm</a>.
</p></blockquote></div>
<!-- ./polynomial/polyint.m -->
<p><a name="doc_002dpolyint"></a>
<div class="defun">
— Function File: <b>polyint</b> (<var>c, k</var>)<var><a name="index-polyint-2047"></a></var><br>
<blockquote><p>Return the coefficients of the integral of the polynomial whose
coefficients are represented by the vector <var>c</var>. The variable
<var>k</var> is the constant of integration, which by default is set to zero.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpoly.html#doc_002dpoly">poly</a>, <a href="doc_002dpolyderiv.html#doc_002dpolyderiv">polyderiv</a>, <a href="doc_002dpolyreduce.html#doc_002dpolyreduce">polyreduce</a>, <a href="doc_002droots.html#doc_002droots">roots</a>, <a href="doc_002dconv.html#doc_002dconv">conv</a>, <a href="doc_002ddeconv.html#doc_002ddeconv">deconv</a>, <a href="doc_002dresidue.html#doc_002dresidue">residue</a>, <a href="doc_002dfilter.html#doc_002dfilter">filter</a>, <a href="doc_002dpolyval.html#doc_002dpolyval">polyval</a>, <a href="doc_002dpolyvalm.html#doc_002dpolyvalm">polyvalm</a>.
</p></blockquote></div>
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