<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>

CC BY-SA 4.0
2023-04-29T21:13:03.510Z
2023-04-29T21:13:03.510Z
cinch
<p><a href="https://i.sstatic.net/mFCT5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/mFCT5.png" alt="enter image description here" /></a></p>
<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>

CC BY-SA 4.0
2023-04-30T20:31:45.293Z
Please, next time, write a title that contains your actual question and is specific.
nbro
<neural-networks><backpropagation><calculus>
What is the partial derivative $\frac{\partial y}{\partial x_1}$ in this neural network?
duanebobby
# 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.  

---

## 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.


---

