title: How does the chain rule work in back propagation?
body: <p>I'm studying neutral networks and I've come across a statement during the derivation of back propagation that I needed help for.</p>
  
  <p><a href="https://i.stack.imgur.com/4ySZX.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/4ySZX.png" alt="enter image description here"></a></p>
  
  <p>My question is if I were to cancel out the common factors in the second form, wouldn't the total sum to k times the original term? Is so, how is it a correct expansion?</p>
  
  <p>PS: The formula was taken from <a href="http://neuralnetworksanddeeplearning.com" rel="nofollow noreferrer">http://neuralnetworksanddeeplearning.com</a></p>