In general, in any neural network, the network tries to learn the weights which can reduce the cost/ loss function. The gradients are updated iteratively by using the derivative of loss function with respect to weights.
Usually for a fix input, calculating gradients of loss with respect to input is not meaningful because if input is fix, then d(loss)/d(Input) is not defined. If the network is feed with 2 different input sequence, in this case you can find the gradient by calculating (Loss2-Loss1)/(X2-X1), where Loss is the value of network loss with respect to input X. There is no use of this while training the network.
Hope it will helps!