Example: Plotting a Function and Its Derivatives

Plots > XY Plots > Plotting Functions > Example: Plotting a Function and Its Derivatives

Use plots to visualize functions and their derivatives.

1. Use the sinc and cos built-in functions to define a new function.

2. Use the prime operator to define two functions to be the first and second derivatives of f.

3. Plot function f and its derivatives. To plot the last two traces, press Shift+Enter twice and type the additional y-axis expressions. You can change the trace style to better differentiate the traces.

<region id="ID0EQHDHB" top="312" left="0" width="452" height="312" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace num-of-points="500">
          <traceStyle color="#FF00008B" symbol="none" line-weight="2" line-style="Solid">lines</traceStyle>
        </trace>
        <trace num-of-points="500">
          <traceStyle color="#FF000000" symbol="none" line-weight="1" line-style="Dash">lines</traceStyle>
        </trace>
        <trace num-of-points="500">
          <traceStyle color="#FFFF0000" symbol="none" line-weight="1" line-style="DashDot">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="ticknumberlock" positionticmark="5" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="ticknumberlock" positionticmark="5" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>f</id>
                  <id>x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>df</id>
                  <id>x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>df2</id>
                  <id>x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <real xmlns="http://schemas.mathsoft.com/math50">1.5</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>