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<a name="Derivatives-_002f-Integrals-_002f-Transforms"></a>
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<a name="Derivatives-_002f-Integrals-_002f-Transforms-1"></a>
<h3 class="section">28.4 Derivatives / Integrals / Transforms</h3>
<p>Octave comes with functions for computing the derivative and the integral
of a polynomial. The functions <code>polyder</code> and <code>polyint</code>
both return new polynomials describing the result. As an example we’ll
compute the definite integral of <em>p(x) = x^2 + 1</em> from 0 to 3.
</p>
<div class="example">
<pre class="example">c = [1, 0, 1];
integral = polyint (c);
area = polyval (integral, 3) - polyval (integral, 0)
⇒ 12
</pre></div>
<a name="XREFpolyder"></a><dl>
<dt><a name="index-polyder"></a><em></em> <strong>polyder</strong> <em>(<var>p</var>)</em></dt>
<dt><a name="index-polyder-1"></a><em>[<var>k</var>] =</em> <strong>polyder</strong> <em>(<var>a</var>, <var>b</var>)</em></dt>
<dt><a name="index-polyder-2"></a><em>[<var>q</var>, <var>d</var>] =</em> <strong>polyder</strong> <em>(<var>b</var>, <var>a</var>)</em></dt>
<dd><p>Return the coefficients of the derivative of the polynomial whose
coefficients are given by the vector <var>p</var>.
</p>
<p>If a pair of polynomials is given, return the derivative of the product
<em><var>a</var>*<var>b</var></em>.
</p>
<p>If two inputs and two outputs are given, return the derivative of the
polynomial quotient <em><var>b</var>/<var>a</var></em>. The quotient numerator is
in <var>q</var> and the denominator in <var>d</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFpolyint">polyint</a>, <a href="Evaluating-Polynomials.html#XREFpolyval">polyval</a>, <a href="Miscellaneous-Functions.html#XREFpolyreduce">polyreduce</a>.
</p></dd></dl>
<a name="XREFpolyint"></a><dl>
<dt><a name="index-polyint"></a><em></em> <strong>polyint</strong> <em>(<var>p</var>)</em></dt>
<dt><a name="index-polyint-1"></a><em></em> <strong>polyint</strong> <em>(<var>p</var>, <var>k</var>)</em></dt>
<dd><p>Return the coefficients of the integral of the polynomial whose
coefficients are represented by the vector <var>p</var>.
</p>
<p>The variable <var>k</var> is the constant of integration, which by default is
set to zero.
</p>
<p><strong>See also:</strong> <a href="#XREFpolyder">polyder</a>, <a href="Evaluating-Polynomials.html#XREFpolyval">polyval</a>.
</p></dd></dl>
<a name="XREFpolyaffine"></a><dl>
<dt><a name="index-polyaffine"></a><em></em> <strong>polyaffine</strong> <em>(<var>f</var>, <var>mu</var>)</em></dt>
<dd><p>Return the coefficients of the polynomial vector <var>f</var> after an affine
transformation.
</p>
<p>If <var>f</var> is the vector representing the polynomial f(x), then
<code><var>g</var> = polyaffine (<var>f</var>, <var>mu</var>)</code> is the vector representing:
</p>
<div class="example">
<pre class="example">g(x) = f( (x - <var>mu</var>(1)) / <var>mu</var>(2) )
</pre></div>
<p><strong>See also:</strong> <a href="Evaluating-Polynomials.html#XREFpolyval">polyval</a>, <a href="Polynomial-Interpolation.html#XREFpolyfit">polyfit</a>.
</p></dd></dl>
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