How to derive the gradient of RNN and what is the definition of Loss function in this graph? I am reading Deep Learning and I am not able to follow the gradient derivation of RNN.
The graph of RNN is like this:

The updating equations are as follow:

The loss function is:

And the derivation of gradient is like this:

I am confused by equation 10.18. 
What is the function of loss here and why this holds:

 A: I hope this will help:
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https://drive.google.com/file/d/0B7TWwiIrcJstZjdWTG84VVF1eDA/view
A: Inspired by this :Softmax and the negative log-likelihood
I write my own Softmax function as:
$$\widehat{y}_i^{(t)}=\frac{e^{o_i^{(t)}}}{\sum_j{e^{o_j^{(t)}}}}$$
and it's derivative with respect to $o_i^{(t)}$:
$$\frac{\partial{\widehat{y}_i^{(t)}}} {\partial{o_i^{(t)}}} =\widehat{y}_i^{(t)}(1-\widehat{y}_i^{(t)})$$
My negative log-likelihood is written as:
$$L^{(t)}=-\sum_{i}\log{\widehat{y}_i^{(t)}}$$
and it's derivative with respect to $\widehat{y}_i^{(t)}$:
$$\frac{\partial{L^{(t)}}}{\partial{\widehat{y}_i^{(t)}}}=-\frac{1}{\widehat{y}_i^{(t)}}$$
Combining the equations above, I get:
$$\frac{\partial{L^{(t)}}}{\partial{o_i^{(t)}}}=\frac{\partial{L^{(t)}}}{\partial{\widehat{y}_i^{(t)}}} \frac{\partial{\widehat{y}_i^{(t)}}}{\partial{o_i^{(t)}}}=-\frac{1}{\widehat{y}_i^{(t)}}[\widehat{y}_i^{(t)}(1-\widehat{y}_i^{(t)})]=\widehat{y}_i^{(t)}-1 $$
I have two questions now:


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*Is my derivation above correct?

*If it is, why is there a small difference between my result and the book Deep Learning :
$$\textbf{1}_{i=y^{(t)}}$$
what dose $\textbf{1}_{i=y^{(t)}}$ mean and can it be just a simple 1 ?
