Answers.Body: <p>From calculus rules: <span class="math-container">$\frac{\partial y}{\partial x_1}=\frac{\partial y}{\partial r_1}\frac{\partial r_1}{\partial x_1}+\frac{\partial y}{\partial r_2}\frac{\partial r_2}{\partial x_1}=3c+d=-6$</span>. In a NN the above 2nd hidden layer where the neurons are not dependent on all the neurons of the previous layer is possible and it's usually just called a non fully-connected layer.</p>
  
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  <p>The answer is supposed to be -6, but I don't know how to get that.</p>
  <p>Also, in a NN, is that 2nd hidden layer possible, where the neurons are not dependent on all the neurons of the previous layer?</p>
  
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Comments.Text: Please, next time, write a title that contains your actual question and is specific.
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Tags: <neural-networks><backpropagation><calculus>
Title: What is the partial derivative $\frac{\partial y}{\partial x_1}$ in this neural network?
UserDisplayName: duanebobby
ThreadText: # What is the partial derivative $\frac{\partial y}{\partial x_1}$ in this neural network?
  
  (Asked by: username_0 on 2023-04-29)
  
  [![enter image description here](https://i.sstatic.net/mFCT5.png)](https://i.sstatic.net/mFCT5.png)
  
  The answer is supposed to be -6, but I don't know how to get that.
  
  Also, in a NN, is that 2nd hidden layer possible, where the neurons are not dependent on all the neurons of the previous layer?
  
  **Tags:** neural-networks, backpropagation, calculus
  
  > **Comments:**
  > **username_1**: Please, next time, write a title that contains your actual question and is specific.  
  
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  ## 1 answers
  
  ### Answer by username_2 on 2023-04-29. Score: 3 | Accepted answer
  
  From calculus rules: $\frac{\partial y}{\partial x\_1}=\frac{\partial y}{\partial r\_1}\frac{\partial r\_1}{\partial x\_1}+\frac{\partial y}{\partial r\_2}\frac{\partial r\_2}{\partial x\_1}=3c+d=-6$. In a NN the above 2nd hidden layer where the neurons are not dependent on all the neurons of the previous layer is possible and it's usually just called a non fully-connected layer.
  
  
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