In this picture, $\hat\theta$ is an unbiased estimator of $\theta$. You may assume 'f(x)' as a standard normal distribution. the second line assume that, if you differentiate $\hat\theta$ by $\theta$, it becomes 0. It means, $\hat\theta$ is just a constant number to $\theta$. But isn't $\hat\theta$ a function of $\theta$? Because it imitates and follows $\theta$. You may say that $$\hat\theta + e = \theta+\epsilon$$ then, it is associated together, so differentiating $\hat\theta$ by $\theta$ will be 1, not 0.
How do you think?