How to calculate the error on the output layer?

Question

Neural networks

Good afternoon!
As I understand it, the error on the output layer for one neuron = (Expected result - the result obtained) * on the derivative activation function.
Question 1
This formula depends on which error function I am using, for example will it be MSE or Cross Entropy?
Question 2
The network error function just shows how accurate the network is and does not affect the output layer error calculation?

Answer 1

It is better to say, not "error function" (error), but "loss function" (loss), which can be the mean square error (MSE), mean absolute error (MAE), cross entropy, etc. Using this function, the difference is estimated the result obtained from the expected. The challenge is to minimize it. Derivatives are needed to calculate the gradient for the subsequent correction of the weights. Gradients are calculated over all elements of the network, starting with the loss function, gradually propagating the error back to the input in the form of weight correction.