A question about the 3.2Section of the paper

[sleep2hours]

Hello! I wonderded this equation when I read this. According to the multivariate chain rule, should it be this:

And if so, how do you derive this section:

[sangminkim-99]

The Eq 5. is changed as below.

Since $\hat{p}$ also depends on $\theta$, you need to use total derivative of $\hat{I}_u$.
Reference: https://en.wikipedia.org/wiki/Total_derivative

Thank you.