Why is backpropagation called backwards propagation of error, when it back propagates error derivatives?
It's actually the error for the neurons. The actual reason for derivation is this:


You find an error then you find the derivative of the error according to some differential equation.
Gradients you obtain using that derivative is basically to determine how much one single neuron in the network made mistake. Gradient at one neuron means if you update the weights or biases according to that you decrease the error network makes.


Backpropagation is the mathematical system for assesing how much one neuron made mistake so you can improve it. Definition is true in that sense.