# Is there a mistake in Lecture 5 of Stanford CS234 available on youtube?

At 53:45 Professor starts to describe temporal difference for linear value function approximation. At 56:20 on slide one can see how weights are updated. Is equation for $$\Delta w$$ correct?

In my opinion thing in brackets should be multiplied by $$X(s) - \gamma X(s')$$ instead of $$X(s)$$ because $$\frac {\partial ( \gamma X(s')^T w )} {\partial w}$$ is not zero. Am i right?

It's the notation that might be a bit confusing. Take a look at David Silver slides: pages 10-15. He has a complete derivation. Do not forget that the term $$r + \gamma V(s';w)$$ is the target. She mentions that in the video and the fact that you are actually doing supervised learning with target provided by a bootstrapped value (you try to minimize the Bellman error).
In other words: you are trying to minimize the error between a target value and the estimation from your model. You do not know the target value so you estimate it with bootstrapping. Then you have $$SE=(y - \hat{y}(w))^2$$. The target y is considered known (as in supervised learning) so eventually you are searching for the weights $$w$$ that will make the output $$\hat{y}$$ of your model close to y. What I wrote here applies for batch training (minimizing the mean square error MSE).
So eventually yes the quantity $$V(s';w)$$ is considered constant and will have derivative 0.