title: Isolating partial derivative from an implicit equation in Mathematica
body: <p>I have a basic problem in Mathematica 11.0 which has puzzled me for a while. I want to calculate <code>y'[x]</code> knowing that <code>Cos[x + Sin[y]] =Sin[y]</code>. I first calculate the derivative w.r.t. <code>x</code> but, when I trie to isolate the partial derivative I get an error message. The code I used is the following:</p>
  
  <p><code>In[23]:= Dt[Cos[x + Sin[y]] ==  Sin[y], x]</code></p>
  
  <p><code>Out[23]= sin(x+sin(y)) (-(cos(y) \[DifferentialD]y/\[DifferentialD]x + 1))==cos(y) \[DifferentialD]y/\[DifferentialD]x</code></p>
  
  <p><code>In[24]:= Solve [%, \[DifferentialD]y/\[DifferentialD]x]</code></p>
  
  <p><code>Error: \[DifferentialD]y/\[DifferentialD]x is not a valid variable.</code></p>
  
  <p>I tried changing the name of <code>\[DifferentialD]y/\[DifferentialD]x</code> too, but it doesn't work neither.</p>