Partial derivative of cross-entropy I am trying to make sense of this question.
$$E(t,o)=-\sum_j t_j \log o_j$$
How did he derive the following?
$$\frac{\partial E} {\partial o_j} = \frac{-t_j}{o_j}$$

You are missing a reformulation Christopher Bishop (1995) took for the cross-entropy, because the formulation
\begin{equation}
E=-\sum_j t_j \log (y_j)
\end{equation}
does not have a minimum value of zero.
However, his reformulation below for cross-entropy error has a minimum value of zero:
\begin{equation}
E=-\sum_j t_j \log \left( \frac{y_j}{t_j} \right).
\end{equation}
For the above equation, the partial derivative of the error $E$ w.r.t $y_j$ is simply
\begin{equation}
\frac{\partial E}{\partial y_j}=-\frac{t_j}{y_j} .
\end{equation}
