title: Plotting a derivative
body: <p>I have an implicit function, and I'm trying to plot the derivative of the solution of this function.</p>
  <p>The function is:</p>
  <pre><code>
  p = \[Phi]/(1/\[Beta]) + ((1 - \[Phi]) \[Phi] (1 - \[Lambda]) \
  \[Beta])/(((W - A) 1/\[Beta] + \[Phi] A/
        p) 1/\[Beta] + \[Phi]*(1 - \[Phi]) A/p)/(
   1/\[Beta] (\[Lambda]/((W - A) 1/\[Beta] + \[Phi] (A/
        p)  ) + (1 - \[Lambda])/(((W - A) 1/\[Beta] + \[Phi] A/
           p) 1/\[Beta] + \[Phi] (1 - \[Phi]) A/p)))
  
  </code></pre>
  <p>And I would like to plot the derivative of the following expression w.r.t <code>\[Phi]</code></p>
  <pre><code>\[Phi]/p ((1-\[Phi]) A + 1/\[Beta] A )
  </code></pre>
  <p>I've been trying to first solve for <code>p</code> explicitly, and plug the solution into the expression above and plot the derivative of the expression, but kept getting an error. My code is :</p>
  <pre><code>Manipulate[
   ans = p /. 
     Solve[p - \[Phi]/(
        1/\[Beta]) - ((1 - \[Phi]) \[Phi] (1 - \[Lambda]) \[Beta])/(((W \
  - A) 1/\[Beta] + \[Phi] A/p) 1/\[Beta] + \[Phi]*(1 - \[Phi]) A/p)/(
        1/\[Beta] (\[Lambda]/((W - A) 1/\[Beta] + \[Phi] (A/
             p)  ) + (1 - \[Lambda])/(((W - A) 1/\[Beta] + \[Phi] A/
                p) 1/\[Beta] + \[Phi] (1 - \[Phi]) A/p))) == 0, p],
   Plot[Evaluate[
     D[f[\[Phi]] == \[Phi]/
        ans[[2]] ((1 - \[Phi]) A + 1/\[Beta] A), \[Phi]]], {\[Phi], 
     0.01, 1}], {A, 10, 500}, {\[Beta], 0.001, 1}, {W, 100, 
    10^9}, {\[Lambda], 0.01, 1}]
  </code></pre>
  <p>The error I'm getting is:</p>
  <pre><code>&quot;Manipulate:Manipulate argument \
  Plot[Evaluate[\!\(\*SubscriptBox[\(\[PartialD]\), \(\[Phi]\)]\((f[\
  \[Phi]] == \((\[Phi]\\\ Power[&lt;&lt;2&gt;&gt;])\)\\\ \((Times[&lt;&lt;2&gt;&gt;] + 
       Times[&lt;&lt;2&gt;&gt;])\))\)\)],{\[Phi],0.01,1}] does not have the correct \
  form for a variable specification&quot;
  </code></pre>
  <p>What am I doing wrong?</p>
  <p>Thank you!</p>